Dario Graffi

Dario Graffi was born in Rovigo, the son of Michele, a yarn wholesale trader and of Amalia Tedeschi. He attended the Istituto tecnico in his home town, specializing in physics and mathematics, but got his diploma in Bologna in 1921, where his family had moved a year before. when he was 20, and in mathematics in 1927, Honors He was awarded the Golden medal "Benemeriti della Scuola, della Cultura, dell'Arte" in 1964, and a year later, the Accademia Nazionale dei Lincei awarded him the Prize of the President of the Italian Republic. ==Work==

Research activity Graffi 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, for his researches in continuum mechanics and for his contribution to oscillation theory. ==Selected publications==

Graffi published 181 works. lists of his publications are included in references and in the biographical section of his "Selected works" (1999, pp. XX–XXVI): however, the set of lecture notes is not listed in any of his publication lists. Scientific works Scientific papers • {{Citation • • . In this paper, 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. • . • , 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. • (online version ). 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. • . 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. • (online version ). In this paper, Graffi introduces the free energy now called Graffi–Volterra free energy after him. • . • . Books • , by (also available with online ), and by (also available with online ). • . A set of lecture notes of a course held by Graffi in the years 1977–1978. • . Dario Graffi's "Selected works", containing a choice of his research papers reprinted in their original typographical form. Historical, commemorative and survey works • . An obituary, with a list of his publications. • . "Electromagnetism in the work of Levi-Civita" (English translation of the contribution title) is a survey of some of the works of Levi-Civita on the theory of electromagnetism. • . The published text of the prolusion to the opening of the 1976 academic year, commemorating Augustin Louis Cauchy and describing his relationships with the Accademia Nazionale di Scienze Lettere e Arti di Modena, the first one in Italy having elected him member. • . "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. ==See also==