Return to Answer

What about a talk on uniqueness theorems for classical solutions? This problem was settled by Emanuele Foà (1929) and David Dolidze (1954), who succeded independently in proving uniqueness for bounded domains (Serrin gives a brief description of their work in [1], p. 251, footnote 1 and [2] p. 271): their proof is nothing more than a clever use of Grönwall's inequality. Later Dario Graffi succeded in extendig their theorem to unbounded domains, under various supplementary conditions. The Wikipedia entries linked above and the main references listed below could give you a basic bibliography: finally, regarding Graffi's contribution, the main reference is [1] which is in Italian, but the topic is also dealt extensively in the monograph [2] (precisely chapter 4), written in English, and which also deals with the results for bounded domains.

Edit

In his comment Calvin Khor has pointed out that a digitized version of [2] is available from the borrowing service of the Internet Archive: I have embedded the link he found into reference [2] and gratefully thank him for the notification.

References

[1] Dario Graffi, "Sul teorema di unicità nella dinamica dei fluidi" [On the uniqueness theorem in fluid mechanics], Annali di Matematica Pura ed Applicata, IV Serie (in Italian), 50: 379–387, (1960), DOI: 10.1007/BF02414524, MR0122198, Zbl 0102.41103.

[2] Dario Graffi, Nonlinear partial differential equations in physical problems, Research Notes in Mathematics, vol. 42, Boston–London–Melbourne: Pitman Advanced Publishing Program, pp. IV+105, ISBN 978-0-273-08474-7, MR0580946, Zbl 0453.35001.

[3] James Serrin, "Mathematical principles of classical fluid mechanics", in Flügge, Siegfried; Truesdell, Clifford A. (eds.), Fluid Dynamics I/Strömungsmechanik I, Handbuch der Physik (Encyclopedia of Physics), vol. VIII/1, Berlin–Heidelberg–New York: Springer-Verlag, pp. 125–263, (1959), DOI: 10.1007/978-3-642-45914-6_2, MR0108116, Zbl 0102.40503.

[4] James Serrin, "On the Uniqueness of Compressible Fluid Motions", Archive for Rational Mechanics and Analysis, 3 (1): pp. 271–288, (1959b), DOI: 10.1007/BF00284180, MR0106646, Zbl 0089.19103.

What about a talk on uniqueness theorems for classical solutions? This problem was settled by Emanuele Foà (1929) and David Dolidze (1954), who succeded independently in proving uniqueness for bounded domains (Serrin gives a brief description of their work in [1], p. 251, footnote 1 and [2] p. 271): their proof is nothing more than a clever use of Grönwall's inequality. Later Dario Graffi succeded in extendig their theorem to unbounded domains, under various supplementary conditions. The Wikipedia entries linked above and the main references listed below could give you a basic bibliography: finally, regarding Graffi's contribution, the main reference is [1] which is in Italian, but the topic is also dealt extensively in the monograph [2] (precisely chapter 4), written in English, and which also deals with the results for bounded domains.

Edit

In his comment Calvin Khor has pointed out that a digitized version of [2] is available from the borrowing service of the Internet Archive: I have embedded the link he found into reference [2] and gratefully thank him for the notification.

References

[1] Dario Graffi, "Sul teorema di unicità nella dinamica dei fluidi" [On the uniqueness theorem in fluid mechanics], Annali di Matematica Pura ed Applicata, IV Serie (in Italian), 50: 379–387, (1960), DOI: 10.1007/BF02414524, MR0122198, Zbl 0102.41103.

[2] Dario Graffi, Nonlinear partial differential equations in physical problems, Research Notes in Mathematics, vol. 42, Boston–London–Melbourne: Pitman Advanced Publishing Program, pp. IV+105, ISBN 978-0-273-08474-7, MR0580946, Zbl 0453.35001.

[3] James Serrin, "Mathematical principles of classical fluid mechanics", in Flügge, Siegfried; Truesdell, Clifford A. (eds.), Fluid Dynamics I/Strömungsmechanik I, Handbuch der Physik (Encyclopedia of Physics), vol. VIII/1, Berlin–Heidelberg–New York: Springer-Verlag, pp. 125–263, (1959), DOI: 10.1007/978-3-642-45914-6_2, MR0108116, Zbl 0102.40503.

[4] James Serrin, "On the Uniqueness of Compressible Fluid Motions", Archive for Rational Mechanics and Analysis, 3 (1): pp. 271–288, (1959b), DOI: 10.1007/BF00284180, MR0106646, Zbl 0089.19103.

What about a talk on uniqueness theorems for classical solutions? This problem was settled by Emanuele Foà (1929) and David Dolidze (1954), who succeded independently in proving uniqueness for bounded domains (Serrin gives a brief description of their work in [1], p. 251, footnote 1 and [2] p. 271): their proof is nothing more than a clever use of Grönwall's inequality. Later Dario Graffi succeded in extendig their theorem to unbounded domains, under various supplementary conditions. The Wikipedia entries linked above and the main references listed below could give you a basic bibliography: finally, regarding Graffi's contribution, the main reference is [1] which is in Italian, but the topic is also dealt extensively in the monograph [2] (precisely chapter 4), written in English, and which also deals with the results for bounded domains.

References

[1] Dario Graffi, "Sul teorema di unicità nella dinamica dei fluidi" [On the uniqueness theorem in fluid mechanics], Annali di Matematica Pura ed Applicata, IV Serie (in Italian), 50: 379–387, (1960), DOI: 10.1007/BF02414524, MR0122198, Zbl 0102.41103.

[2] Dario Graffi, Nonlinear partial differential equations in physical problems, Research Notes in Mathematics, vol. 42, Boston–London–Melbourne: Pitman Advanced Publishing Program, pp. IV+105, ISBN 978-0-273-08474-7, MR0580946, Zbl 0453.35001.

[3] James Serrin, "Mathematical principles of classical fluid mechanics", in Flügge, Siegfried; Truesdell, Clifford A. (eds.), Fluid Dynamics I/Strömungsmechanik I, Handbuch der Physik (Encyclopedia of Physics), vol. VIII/1, Berlin–Heidelberg–New York: Springer-Verlag, pp. 125–263, (1959), DOI: 10.1007/978-3-642-45914-6_2, MR0108116, Zbl 0102.40503.

[4] James Serrin, "On the Uniqueness of Compressible Fluid Motions", Archive for Rational Mechanics and Analysis, 3 (1): pp. 271–288, (1959b), DOI: 10.1007/BF00284180, MR0106646, Zbl 0089.19103.

What about a talk on uniqueness theorems for classical solutions? This problem was settled by Emanuele Foà (1929) and David Dolidze (1954), who succeded independently in proving uniqueness for bounded domains (Serrin gives a brief description of their work in [1], p. 251, footnote 1 and [2] p. 271): their proof is nothing more than a clever use of Grönwall's inequality. Later Dario Graffi succeded in extendig their theorem to unbounded domains, under various supplementary conditions. The Wikipedia entries linked above and the main references listed below could give you a basic bibliography: finally, regarding Graffi's contribution, the main reference is [1] which is in Italian, but the topic is also dealt extensively in the monograph [2] (precisely chapter 4), written in English, and which also deals with the results for bounded domains.

Edit

In his comment Calvin Khor has pointed out that a digitized version of [2] is available from the borrowing service of the Internet Archive: I have embedded the link he found into reference [2] and gratefully thank him for the notification.

References

[1] Dario Graffi, "Sul teorema di unicità nella dinamica dei fluidi" [On the uniqueness theorem in fluid mechanics], Annali di Matematica Pura ed Applicata, IV Serie (in Italian), 50: 379–387, (1960), DOI: 10.1007/BF02414524, MR0122198, Zbl 0102.41103.

[2] Dario Graffi, Nonlinear partial differential equations in physical problems, Research Notes in Mathematics, vol. 42, Boston–London–Melbourne: Pitman Advanced Publishing Program, pp. IV+105, ISBN 978-0-273-08474-7, MR0580946, Zbl 0453.35001.

[3] James Serrin, "Mathematical principles of classical fluid mechanics", in Flügge, Siegfried; Truesdell, Clifford A. (eds.), Fluid Dynamics I/Strömungsmechanik I, Handbuch der Physik (Encyclopedia of Physics), vol. VIII/1, Berlin–Heidelberg–New York: Springer-Verlag, pp. 125–263, (1959), DOI: 10.1007/978-3-642-45914-6_2, MR0108116, Zbl 0102.40503.

[4] James Serrin, "On the Uniqueness of Compressible Fluid Motions", Archive for Rational Mechanics and Analysis, 3 (1): pp. 271–288, (1959b), DOI: 10.1007/BF00284180, MR0106646, Zbl 0089.19103.

What about a talk on uniqueness theorems for classical solutions? This problem was settled by Emanuele Foà (1929) and David Dolidze (1954), who succeded independently in proving uniqueness for bounded domains (Serrin gives a brief description of their work in [1], p. 251, footnote 1 and [2] p. 271): their proof is nothing more than a clever use of Grönwall's inequality. Later Dario Graffi succeded in extendig their theorem to unbounded domains, under various supplementary conditions. The Wikipedia entries linked above and the main references listed below could give you a basic bibliography: finally, regarding Graffi's contribution, the main reference is [1] which is in Italian, but the topic is also dealt extensively in the monograph [2] (precisely chapter 4), written in English.

References

[1] Dario Graffi, "Sul teorema di unicità nella dinamica dei fluidi" [On the uniqueness theorem in fluid mechanics], Annali di Matematica Pura ed Applicata, IV Serie (in Italian), 50: 379–387, (1960), DOI: 10.1007/BF02414524, MR0122198, Zbl 0102.41103.

[2] Dario Graffi, Nonlinear partial differential equations in physical problems, Research Notes in Mathematics, vol. 42, Boston–London–Melbourne: Pitman Advanced Publishing Program, pp. IV+105, ISBN 978-0-273-08474-7, MR0580946, Zbl 0453.35001.

[3] James Serrin, "Mathematical principles of classical fluid mechanics", in Flügge, Siegfried; Truesdell, Clifford A. (eds.), Fluid Dynamics I/Strömungsmechanik I, Handbuch der Physik (Encyclopedia of Physics), vol. VIII/1, Berlin–Heidelberg–New York: Springer-Verlag, pp. 125–263, (1959), DOI: 10.1007/978-3-642-45914-6_2, MR0108116, Zbl 0102.40503.

[4] James Serrin, "On the Uniqueness of Compressible Fluid Motions", Archive for Rational Mechanics and Analysis, 3 (1): pp. 271–288, (1959b), DOI: 10.1007/BF00284180, MR0106646, Zbl 0089.19103.

What about a talk on uniqueness theorems for classical solutions? This problem was settled by Emanuele Foà (1929) and David Dolidze (1954), who succeded independently in proving uniqueness for bounded domains (Serrin gives a brief description of their work in [1], p. 251, footnote 1 and [2] p. 271): their proof is nothing more than a clever use of Grönwall's inequality. Later Dario Graffi succeded in extendig their theorem to unbounded domains, under various supplementary conditions. The Wikipedia entries linked above and the main references listed below could give you a basic bibliography: finally, regarding Graffi's contribution, the main reference is [1] which is in Italian, but the topic is also dealt extensively in the monograph [2] (precisely chapter 4), written in English, and which also deals with the results for bounded domains.

References

[1] Dario Graffi, "Sul teorema di unicità nella dinamica dei fluidi" [On the uniqueness theorem in fluid mechanics], Annali di Matematica Pura ed Applicata, IV Serie (in Italian), 50: 379–387, (1960), DOI: 10.1007/BF02414524, MR0122198, Zbl 0102.41103.

[2] Dario Graffi, Nonlinear partial differential equations in physical problems, Research Notes in Mathematics, vol. 42, Boston–London–Melbourne: Pitman Advanced Publishing Program, pp. IV+105, ISBN 978-0-273-08474-7, MR0580946, Zbl 0453.35001.

[3] James Serrin, "Mathematical principles of classical fluid mechanics", in Flügge, Siegfried; Truesdell, Clifford A. (eds.), Fluid Dynamics I/Strömungsmechanik I, Handbuch der Physik (Encyclopedia of Physics), vol. VIII/1, Berlin–Heidelberg–New York: Springer-Verlag, pp. 125–263, (1959), DOI: 10.1007/978-3-642-45914-6_2, MR0108116, Zbl 0102.40503.

[4] James Serrin, "On the Uniqueness of Compressible Fluid Motions", Archive for Rational Mechanics and Analysis, 3 (1): pp. 271–288, (1959b), DOI: 10.1007/BF00284180, MR0106646, Zbl 0089.19103.