Dario Graffi

Dario Graffi
Born	January 10, 1905 Rovigo
Died	December 28, 1990 (aged 85) Bologna
Nationality	Italian
Fields	Continuum mechanics Theory of electromagnetism Fluid dynamics Oscillation theory
Doctoral advisor	Pietro Buzano
Other academic advisors	Quirino Majorana Emanuele Foà
Notable students	Lamberto Cesari Ercole De Castro Mauro Fabrizio

Dario Graffi (10 January 1905 – 28 December 1990) was an influential Italian mathematical physicist. He is known for his researches on the Electromagnetic field, particularly for a mathematical explanation of the Luxemburg effect, for proving an important uniqueness theorem for the solutions of a class of fluid dynamics equations including the Navier-Stokes equation,^[1] for his researches in continuum mechanics and for his contribution to oscillation theory.

Selected works

• Graffi, Dario (1936), "Una teoria ereditaria dell'effetto Lussemburgo", Rendiconti del Seminario Matematico della Università di Padova (in Italian) 7: 36–54, JFM 62.0546.02, Zbl 0015.13705. In the paper "An hereditary theory of the Luxemburg effect" (English translation of the title), written only few years after the discovery of the effect itself, Dario Graffi proposes a theory of the Luxemburg effect based on Volterra's theory of hereditary phenomena.
• Graffi, Dario (1953), "Il Teorema di Unicita nella Dinamica dei Fluidi Compressibili", Journal of Rational Mechanics and Analysis (in Italian) 2 (1): 99–106, doi:10.1512/iumj.1953.2.52004, ISSN 0022-2518, MR 0052270, Zbl 0050.19604. In the paper "The uniqueness theorem in the dynamics of compressible fluids" (English translation of the title) 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.^[2]
• Graffi, Dario (1955), "Il teorema di unicità per i fluidi incompressibili, perfetti, eterogenei" (PDF), Revista de la Unión Matemática Argentina y de la Asociación Física Argentina (in Italian) XVII: 73–77, ISSN 0041-6932, MR 0082829, Zbl 0074.20206.
• Graffi, Dario (2 November 1959), "Sur un théorème d'unicité pour le mouvement d'un fluide visqueux dans un domaine illimité", Comptes rendus hebdomadaires des séances de l'Académie des sciences (in French) 249 (2): 1741–1743, MR 0109550, Zbl 0088.41201, 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", Annali di Matematica Pura ed Applicata, IV Serie (in Italian) 50: 379–387, doi:10.1007/BF02414524, MR 122198, Zbl 0102.41103. In the paper "On the uniqueness theorem in fluid mechanics" (English translation of the title) 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", Rendiconti del Seminario Matematico e Fisico di Milano (in Italian) 32 (1): 80–91, doi:10.1007/BF02925666, MR 0148304, Zbl 0128.43503. "On uniqueness theorems in fluid dynamics" is the published text of a conference held at the Seminario Matematico e Fisico di Milano, exposing mainly his researches on the uniqueness of the solutions to the Navier-Stokes equations.
• Graffi, Dario (1981), Questioni sull'elettromagnetismo (in Italian), Napoli: Liguori editore, p. 247, ISBN 88-207-1136-2. "Issues on electromagnetism" (English translation of the title) is a set of published lecture notes of a course held by Graffi in the years 1977–1978.
• Graffi, Dario (1992), "L'opera di Vito Volterra sui fenomeni ereditari e alcune sue conseguenze", in Amaldi, E.; Amerio, L.; Fichera, G.; Gregory, T.; Grioli, G.; Martinelli, E.; Montalenti, G.; Pignedoli, A.; Salvini, Giorgio; Scorza Dragoni, Giuseppe, Convegno internazionale in memoria di Vito Volterra (8–11 ottobre 1990), Atti dei Convegni Lincei (in Italian) 92, Roma: Accademia Nazionale dei Lincei, pp. 39–76, ISSN 0391-805X, MR 1783028, Zbl 0977.01022. "The work of Vito Volterra on hereditary phenomena and some of their consequences" is an ample technical survey paper on the research work of Vito Volterra on hereditary phenomena in mathematical physics.
• Graffi, Dario (November 1999), Fabrizio, M.; Grioli, G.; Renno, P., eds., Opere scelte (in Italian), Bologna: C.N.R. – Gruppo Nazionale per la Fisica Matematica, pp. XXXII+458. Dario Graffi's "Selected works", containing a choice of his research papers: the works are written in Italian, English and French and are reprinted in their original typographical form.

See also

• Gaetano Fichera
• Heat equation
• Ordinary differential equation
• Wave propagation

Notes

1. See for example (Serrin 1963, §5).
2. See (Serrin 1959, p. 251, footnote 1).

References

Biographical references

• Accademia delle Scienze di Torino (2013), Dario GRAFFI, Accademia delle Scienze di Torino, retrieved 22 June 2014.
• Accademia Nazionale dei Lincei (2012), Annuario dell'Accademia Nazionale dei Lincei 2012 – CDX dalla Sua Fondazione (PDF) (in Italian), Roma: Accademia Nazionale dei Lincei, p. 734. The "Yearbook" of the renowned Italian scientific institution, including an historical sketch of its history, the list of all past and present members as well as a wealth of informations about its academic and scientific activities.
• Barbieri, Francesco; Taddei, Ferdinando (2006), L’Accademia di Scienze, Lettere e Arti di Modena dalle origini (1683) al 2005. Tomo I – La storia e i soci (PDF) (in Italian), Modena: Mucchi Editore, p. 359, ISBN 88-7000-419-8. The first part ("Tomo") of an extensive work on the "Accademia di Scienze, Lettere e Arti di Modena", reporting the history of the academy and biographies of members up to the year 2006.
• Consiglio Scientifico del G.N.F.M. (November 1999), "Dario Graffi", in Fabrizio, M.; Grioli, G.; Renno, P., Opere scelte (in Italian), Bologna: C.N.R. – Gruppo Nazionale per la Fisica Matematica, pp. XI–XXXII.

Scientific references

• Capitani, Ovidio; Capriz, Gianfranco; Caputo, Michele; Fabrizio, Mauro; Graffi, Sandro; Grioli, Giuseppe; Podio Guidugli, Paolo; Renno, Pasquale, eds. (2002), Nuovi progressi nella fisica matematica dall'eredità di Dario Graffi – Convegno Internazionale (Bologna, 24–27 maggio 2000), Atti dei Convegni Lincei 177, Roma: Accademia Nazionale dei Lincei, p. 304, ISBN 88-218-0868-8, ISSN 0391-805X. The proceedings of the international congress "New advances in mathematical physics from Dario Graffi's heritage", held in Bologna on May 24–27, 2000, at the Accademia delle Scienze dell'Istituto di Bologna, under the auspices of the Accademia Nazionale dei Lincei.
• Fabrizio, Mauro (1994), "Su alcune importanti ricerche di Dario Graffi", Atti e Memorie della Accademia Nazionale di Scienze Lettere e Arti di Modena, Serie VII (in Italian), X (1992–93): 23–27. "On some important researches of Dario Graffi" (English translation of the title) is a short commemoration reviewing Graffi's contribution to continuum physics, specifically to elasticity, electromagnetism and the mathematical theory of hereditary phenomena.
• Fabrizio, Mauro (2012), "Dario Graffi in a Complex Historical Period", in Coen, Salvatore, Mathematicians in Bologna 1861–1960, Basel: Birkhäuser, pp. 179–195, doi:10.1007/978-3-0348-0227-7_7, ISBN 978-3-0348-0226-0, MR 2934582.
• Franchi, Franca; Straughan, Brian (2002), "Convection, diffusion and pollution: the model of Dario Graffi", in Capitani, Ovidio; Capriz, Gianfranco; Caputo, Michele; Fabrizio, Mauro; Graffi, Sandro; Grioli, Giuseppe; Podio Guidugli, Paolo; Renno, Pasquale, Nuovi progressi nella fisica matematica dall'eredità di Dario Graffi – Convegno Internazionale (Bologna, 24–27 maggio 2000), Atti dei Convegni Lincei 177, Roma: Accademia Nazionale dei Lincei, pp. 257–265, ISBN 88-218-0868-8, ISSN 0391-805X.
• Nardini, Renato (1994), "Una sintesi dell'opera scientifica di Dario Graffi", Atti e Memorie della Accademia Nazionale di Scienze Lettere e Arti di Modena, Serie VII (in Italian), X (1992–93): 19–22. "A synthesis of the scientific work of Dario Graffi" (English translation of the title) is a short commemorative review of Graffi's scientific contributions.
• 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, MR 0108116, Zbl 0102.40503.
• 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., Madison: The University of Wisconsin Press, pp. 69–98, MR 0150444, Zbl 0115.08502.