Emanuele Foà

Short description: Italian engineer and physicist (1892–1949)

Emanuele Foà

Born| (1892-08-16)16 August 1892[1]

Savigliano

Died| 9 October 1949(1949-10-09) (aged 57)

Bologna

Nationality| Italian
Alma mater| Politecnico di Torino (1919)
Known for|

* Theory of Navier–Stokes equations
* Heat conduction theory

Scientific career
Fields|

* Engineering physics
* Fluid dynamics

Institutions|

* Politecnico di Torino
* Università degli Studi di Bologna

Academic advisors| Benedetto Luigi Montel[2]
Notable students| Dario Graffi

Emanuele Foà (16 August 1892[1] – 9 October 1949) was an Italian engineer and engineering physicist, known for his contribution to mathematical fluid dynamics. In particular he proved the first known uniqueness theorem for the solutions to the three-dimensional Navier–Stokes equations for incompressible fluids in bounded domains.[3]

## Contents

* 1 Life and academic career
* 1.1 The years from 1938 to 1945: the "Italian Racial Laws" and the World War II
* 1.2 Honors
* 2 Work
* 2.1 Teaching activity
* 2.2 Research activity
* 3 Selected publications
* 4 See also
* 5 Notes
* 6 References
* 6.1 Biographical and general references
* 6.2 Scientific references
* 7 External links

## Life and academic career

He was born in Savigliano, in a Jewish family of distinguished professionals and officials:[4] his father, Teodoro Foà, was a military physician serving as a major the Royal Italian Army,[5] who died at the age of 42 due to the viral fevers he contracted during the Eritrea war campaign.[4] Despite having lost his father at a young age and having a disabled sister,[6] he succeeded in studying engineering at the Polytechnic University of Turin thanks to a scholarship.[7] The outbreak of World War I in Italy in 1915 forced him to interrupt his engineering studies: he joined the army and served as an artillery officer for the years 1916 and 1917.[5] On 28 October 1917, during the battle of Caporetto, he was taken prisoner and spent a year in a prisoner camp located in Germany.[5][8]

At the end of the war, notwithstanding his health problems, he successfully completed his university studies: he got his Laurea degree in industrial engineering at the Polytechnic University of Turin in August 1919.[9] From 1 December 1919 he started to work at his alma mater,[10] as assistant professor to the chair of thermal engineering,[11] which at the time was held by Benedetto Luigi Montel.[2] In 1927 he participated and won a competitive examination for a professorship in engineering physics at the then called "Royal School of Engineering of Bologna":[12] in 1928 he left Turin for Bologna,[13] succeeding, after a brief time period, to Luigi Donati who had held the chair for several decades.[14] The very same year he met Dario Graffi, who had earlier become assistant professor to the chair of engineering physics:[15] their cordial relations became over time a deep and tenacious friendship, lasted until Foà's death.[16]

In Bologna, he passionately devoted himself to teaching as his course handouts, published in several editions, testify:[17] the same time was fruitful for his researches activity,[18] and in 1930 he was appointed ordinary professor.[6]

### The years from 1938 to 1945: the "Italian Racial Laws" and the World War II

His teaching at the university was interrupted in 1938, the year the Italian Government approved the "Racial Laws", "unreasonable, before being unjust".[19] Forced by the law to an early retirement, the Council of the faculty of engineering substituted him with Graffi: he was very happy with the council choice,[6] due to their friendship and mutual esteem.[20] For his part Graffi, who could not adopt Foà's handouts due to prohibition imposed by the laws on publications by Jewish authors, published them under his name:[6] cautiously, he kept sending to Foà's house students for private lessons, in order to help him supplement his small retirement pension.[21]

During World War II period, Foà and his wife managed to stay in Bologna but had to change their accommodation frequently, being hosted by friendly families.[22] In October 1943, being warned by Dino Zanobetti about a raid of the police, he and his wife left their house and went to an apartment made available by Dante Piccioli, a wealthy engineer and friend of them.[23] More than a month later, on 7 December, Bologna was bombed and the apartment where Foà and his wife resided was destroyed:[24] being at home,[25] Foà was severely wounded at the right leg and was brought to the Sant'Orsola Hospital.[26]

### Honors

In 1933 he was elected corresponding member of the Accademia delle Scienze dell'Istituto di Bologna[27] and, after being reintegrated in his role of professor at the University of Bologna in 1945,[28] he became ordinary member in 1947.[29] Also in 1947, jointly with some fellow engineers, he founded the Bologna Section of the Associazione Termotecnica Italiana,[28][30] and was elected as his first president.[28]

## Work

### Teaching activity

> Si dedicò all'insegnamento con grande passione, lo provano i suoi corsi di dispense di cui si fecero diverse edizioni e in cui si manifesta la sua personalità didattica ad un tempo profonda e semplificatrice.[31]

> --Dario Graffi, (Graffi 1949–1950)

### Research activity

> Al primo periodo bolognese del Foà sono soprattutto da ascriversi le importanti ricerche sull'analisi dimensionale e sulle sue applicazioni allo studio dei processi tecnici in vista di dedurre, da tali analisi, metodi semplici e sicuri per stabilire importanti proprietà delle equazioni differenziali che tali processi reggono, pur senza integrarle.[32]

> --Paolo Dore, (Dore 1952)

## Selected publications

* Foà, Emanuele (January 1926), "Sulla legge di variazione dell'effetto Volta in funzione della temperatura" (in it), Il Nuovo Cimento 3 (1): 49–66, doi:10.1007/BF02961052, Bibcode: 1926NCim....3...49F .
* Foà, Emanuele (January 1926a), "Sulla esperienza di Désormes e Clément" (in it), Il Nuovo Cimento 3 (1): 101–113, doi:10.1007/BF02961056, Bibcode: 1926NCim....3..101F .
* Foà, Emanuele (31 December 1929), "Sull'impiego della analisi dimensionale nello studio del moto turbolento. – Prima nota" (in it), L'Industria: rivista tecnica ed economica illustrata XLIII (24): 426–431, http://digitale.bnc.roma.sbn.it/tecadigitale/giornale/CFI0356408/1929/unico . In this article Foà proves his uniqueness theorem for classical solutions to the Navier-Stokes equation.
* Foà, Emanuele (30 April 1930), "Sull'impiego della analisi dimensionale nello studio del moto turbolento. – Seconda nota" (in it), L'Industria: rivista tecnica ed economica illustrata XLIV (8): 203–226, http://digitale.bnc.roma.sbn.it/tecadigitale/visore/#/main/viewer?idMetadato=7446281&type=bncr . This is the companion paper to (Foà 1929), where Foà describes his rigorous approach to dimensional analysis.
* Foà, Emanuele (October 1930), "Sulla trasmissione di calore per irradiamento. Prima nota" (in it), Il Politecnico LXXVIII (10): 601–604, http://emeroteca.braidense.it/eva/sfoglia_articolo.php?IDTestata=120&CodScheda=216&CodVolume=2649&CodFascicolo=17944&CodArticolo=321717 .
* Foà, Emanuele (January 1931), "Sulla trasmissione di calore per irradiamento. Seconda nota" (in it), Il Politecnico LXXIX (1): 23–32, http://emeroteca.braidense.it/eva/sfoglia_articolo.php?IDTestata=120&CodScheda=216&CodVolume=2650&CodFascicolo=17950&CodArticolo=321973 .
* Foà, Emanuele (1948), "Sulla trasmissione del calore in mezzi isotropi o anisotropi con coefficiente di conduttività variabile con la temperatura" (in it), Memorie dell'Accademia delle Scienze dell'Istituto di Bologna, Classe di Scienze Fisiche, Serie X 4: 119–122 .
* Foà, Emanuele (1951), Giulianini, Arturo, ed. (in it), Fondamenti di termodinamica, Manuali scientifici Zanichelli, Bologna: Zanichelli Editore, pp. XVI+255, http://www.catalogo.zanichelli.it/Pages/Opera?siteLang=IT&id_opera=0000000007303 , also reviewed by Mandò, Manlio (December 1951), "Emanuele Foà: Fondamenti di Termodinamica" (in it), Il Nuovo Cimento 8 (12): 1017–1018, doi:10.1007/BF02781954, Bibcode: 1951NCim....8.1017M .

## See also

* David Dolidze
* Euler equations
* Fluid mechanics
* Olga Ladyzhenskaya
* James Serrin

## Notes

1. ↑ 1.0 1.1 There is an uncertainty on the month of his birth. While (Dore 1952) and (Graffi 1949–1950) assert that he was born on August, (Codegone 1949) states that the month of his birth is July: however, even in this latter reference, at the top of the second column of page 443, Foà's birth date is reported to be 16 August 1892, therefore this one is considered to be correct.
2. ↑ 2.0 2.1 According to Codegone (1949, p. 443, 1970, p. 34 and Ref. [28]) and (Dore 1952).
3. ↑ (Serrin 1959).
4. ↑ 4.0 4.1 (Codegone 1949).
5. ↑ 5.0 5.1 5.2 See (Graffi 1949–1950), (Dore 1952) and (Codegone 1949).
6. ↑ 6.0 6.1 6.2 6.3 (Zanobetti 2002).
7. ↑ According to (Graffi 1949–1950).
8. ↑ According to (Dore 1952), the harshness of the camp conditions seriously undermined his health.
9. ↑ According to (Codegone 1949) and (Graffi 1949–1950): (Dore 1952) gives only the basic information.
10. ↑ According to (Codegone 1949): (Graffi 1949–1950) writes that he started on an unspecified day of November 1919.
11. ↑ Precisely, to the chair of "Termotecnica" (Codegone 1949), (Graffi 1949–1950).
12. ↑ As reported by Codegone (1949, p. 443, 1970, p. 34 and Ref. [28]).
13. ↑ See (Garelli 1929), (Dore 1952) and (Graffi 1949–1950). (Graffi 1949–1950) also says that Foà held the chair from January 1928.
14. ↑ According to (Dore 1952). Also (Zanobetti 2002) briefly mentions this detail.
15. ↑ As recalled by (Graffi 1949–1950) himself.
16. ↑ In the exact words of (Graffi 1949–1950), "Subito, per Sua cortesia, si stabilì tra me e lui quella cordialità di rapporti che più tardi doveva mutarsi in profonda e tenace amicizia" (English translation: "Immediately, for His kindness, that cordiality of relations between him and me that later had to change into a deep and tenacious friendship was established"). Also (Zanobetti 2002) recalls briefly their friendship and mutual respect.
17. ↑ According to (Graffi 1949–1950): see also the "Teaching activity" section of this entry.
18. ↑ According to (Codegone 1949): see also the "Research activity" section of this entry.
19. ↑ This sentence is reported by both (Codegone 1949) and (Graffi 1949–1950): this latter one further remarks "... come fu detto ottimamente, ..." (English translation: "... as it was well said, ...").
20. ↑ (Graffi 1949–1950), (Zanobetti 2002).
21. ↑ (Zanobetti 2002) describes in detail the life of Foà and his family during this period: (Graffi 1949–1950) and (Codegone 1949) mention briefly the private lessons he gave to students coming to his house.
22. ↑ (Graffi 1949–1950), (Codegone 1949).
23. ↑ Zanobetti met Foà after being informed via a phone call by Graffi that he was still in Bologna: the episode is narrated in detail in (Zanobetti 2002).
24. ↑ (Zanobetti 2002).
25. ↑ They did not go to the air-raid shelters, as (Zanobetti 2002) remarks, because they did not want to risk of being recognized, arrested and deported.
26. ↑ Following (Zanobetti 2002). (Graffi 1949–1950) and (Codegone 1949) write very briefly of Foà wounded leg and also give a different version, postponing the event in January 1944.
27. ↑ (Graffi 1949–1950).
28. ↑ 28.0 28.1 28.2 See (Codegone 1949).
29. ↑ According to (Codegone 1949) and (Graffi 1949–1950), who states also the year of his election. Precisely, he became "Accademico Benedettino" i.e. literally "Benedictine Academician", as this is the way every ordinary member of the Academy of Sciences of the Institute of Bologna is called.
30. ↑ The "Associazione Termotecnica Italiana" is the professional society of Italian thermal engineers.
31. ↑ (English translation) "He devoted himself to teaching with great passion, and this is proved by its courses handouts which had several editions and which show his teaching personality, at once profound and simplifying."
32. ↑ (English translation) "To the first Bolognese period of Foà are to be ascribed important researches on dimensional analysis and its applications to the study of technical processes aimed to deduce, from such analyses, simple and safe methods to establish important properties of the differential equations governing such processes, though not integrating them."

## References

### Biographical and general references

* Cocchi, Alessandro (12 April 2016), Il gabinetto di Fisica Tecnica dell'Ateneo bolognese: le origini, la struttura, la ricerca, gli uomini, Bologna: ALMA MATER STUDIORUM - UNIVERSITÀ DI BOLOGNA, pp. 49 . The slides of a conference held by Alessandro Cocchi, emeritus professor of engineering physics at the University of Bologna, on the history of the Laboratory of Engineering Physics of the University.
* Codegone, Cesare (1949), "Emanuele Foà" (in it), La Termotecnica 11: 443–445 . An obituary written by one of his fellow students at the Polytechnic University of Turin, with a list of his publications.
* Codegone, Cesare (1970), "Contributo alla storia della fisica tecnica in Italia", XXV Congresso Nazionale ATI. Memorie, Trieste: Associazione Termotecnica Italiana, pp. 164, https://inis.iaea.org/search/download.aspx?RN=2006069&redURL=http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/02/006/2006069.pdf . "Contribution to the history of Engineering Physics in Italy" is a short historical survey giving details on life and work of several Italian scholars on Engineering Physics.
* Dore, Paolo (1952), "Emanuele Foà", in Università di Bologna (in it), Annuario degli anni accademici 1948–1949 – 1949–1950, Bologna: Tipografia Compositori per conto dell'Università degli Studi di Bologna, pp. 158–159, http://amshistorica.unibo.it/archivio/000196/000003/000162.jpg . A short obituary written by the Dean of the Faculty of Engineering at the University of Bologna, for the "Yearboook of the Academic years 1948–1949 – 1949–1950": a photograph of Foà is included.
* Garelli, Felice (1929), "Solenne Inaugurazione dell'Anno Accademico 1928–1929" (in it), Annuario della Reale Scuola di Ingegneria (Reale Politecnico) di Torino, Anno accademico 1928–1929, Torino: Tipografia E. Schioppo per conto della Reale Scuola di Ingegneria di Torino, pp. 7–15, http://digit.biblio.polito.it/3280/1/annuario 1928-1929.pdf#page=3&pagemode=bookmarks . The Inaugural Address of the director of the Polytechnic University of Turin, for the "Yearboook of the Academic Year 1928–1929".
* Graffi, Dario (1949–1950), "Emanuele Foà" (in it), Rendiconto delle Sessioni dell'Accademia delle Scienze dell'Istituto di Bologna, Classe di Scienze Fisiche, nuova serie LIV: 46–54 . An obituary, with a list of his publications.
* Zanobetti, Dino (2002), "Giulio Supino e Emanuele Foà", in Mirri, Domenico; Arienti, Stefano (in it), La cattedra negata. Dal giuramento di fedeltà al fascismo alle leggi razziali nell'Università di Bologna, Bologna: CLUEB, pp. 85–94, doi:10.1400/34421, ISBN 88-491-1848-1, http://digital.casalini.it/8849118481 . Recollections of Giulio Supino and Emanuele Foà by Dino Zanobetti, professor emeritus of Electrical engineering and one of their former students.

### Scientific references

* Graffi, Dario (1953), "Il Teorema di Unicita nella Dinamica dei Fluidi Compressibili" (in it), Journal of Rational Mechanics and Analysis 2 (1): 99–106, doi:10.1512/iumj.1953.2.52004, ISSN 0022-2518 . In this article Graffi extends to compressible viscous fluids a uniqueness theorem for the solutions to Navier-Stokes equation in bounded domains, previously proved only for incompressible fluids by Emanuele Foà and rediscovered by David Dolidze.
* Graffi, Dario (2 November 1959), "Sur un théorème d'unicité pour le mouvement d'un fluide visqueux dans un domaine illimité" (in fr), Comptes rendus hebdomadaires des séances de l'Académie des sciences 249 (2): 1741–1743, http://gallica.bnf.fr/ark:/12148/bpt6k731d/f603.image , available at Gallica. A short research note announcing the results of the author on the uniqueness of solutions of the Navier-Stokes equations on unbounded domains under the hypothesis of constant fluid velocity at infinity.
* Graffi, Dario (1960), "Sul teorema di unicità nella dinamica dei fluidi" (in it), Annali di Matematica Pura ed Applicata, IV Serie 50: 379–387, doi:10.1007/BF02414524 . In this paper Graffi extends his uniqueness theorem for the solutions of Navier-Stokes equations on unbounded domains relaxing previously assumed hypotheses on the behaviour of the velocity at infinity.
* Graffi, Dario (1962), "Sui teoremi di unicita nella dinamica dei fluidi" (in it), Rendiconti del Seminario Matematico e Fisico di Milano 32 (1): 80–91, doi:10.1007/BF02925666 . This article is the published text of a conference Graffi held at the Seminario Matematico e Fisico di Milano, exposing mainly his researches on the uniqueness of the solutions to the Navier-Stokes equations.
* Serrin, James (1959), "Mathematical principles of classical fluid mechanics", in Flügge, Siegfried; Truesdell, Clifford A., Fluid Dynamics I/Strömungsmechanik I, Handbuch der Physik (Encyclopedia of Physics), VIII/1, Berlin–Heidelberg–New York: Springer-Verlag, pp. 125–263, doi:10.1007/978-3-642-45914-6_2, ISBN 978-3-642-45916-0, Bibcode: 1959HDP.....8..125S .
* Serrin, James (1963), "The initial Value problem for the Navier-Stokes equations", in Langer, Rudolph E., Nonlinear problems. Proceedings of a symposium conducted by the Mathematics Research Center, United States Army, at the University of Wisconsin, Madison, April 30-May 2, 1962., The University of Wisconsin Press, pp. 69–98 .

## External links

* Pozzato, Enzo (1997), "FOÀ, Emanuele" (in it), Enciclopedia Treccani, Dizionario Biografico degli Italiani, XLVIII, http://www.treccani.it/enciclopedia/emanuele-foa_(Dizionario_Biografico)/ . The biographical entry about Emanuele Foà in the "Dizionario Biografico degli Italiani (Biographical Dictionary of Italians)" section of the Enciclopedia Treccani.

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