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An alternative proof of Di Perna’s theorem. (English) Zbl 0763.35056

We simplify Serre’s approach [D. Serre, J. Math. Pures Appl., IX. Ser. 65, 423-468 (1986; Zbl 0601.35070)] and extend it to equations such as those for flow that is not subsonic.

MSC:

35L60 First-order nonlinear hyperbolic equations
76G25 General aerodynamics and subsonic flows
76H05 Transonic flows

Citations:

Zbl 0601.35070
Full Text: DOI

References:

[1] Di Perna, Arch. Rat. Mech. Anal. 82 pp 27– (1983)
[2] Murat, Ann. Scuola Norm. Sup. Pisa 5 pp 489– (1978)
[3] Compensated compactness and applications to partial differential equations, Nonlinear Analysis and Mechanics, Herriot-Watt Symposium IV, 1979, pp. 136–192, Research Notes in Mathematics, Pitman, Edinburgh.
[4] Serre, Jour. de Math. Pures et App. 65 pp 423– (1986)
[5] Morawetz, Comm. Pure Appl. Math. 38 pp 797– (1985)
[6] Friedrichs, Comm. Pure Appl. Math. 11 pp 333– (1958)
[7] Morawetz, Comm. Pure Appl. Math. 11 pp 315– (1958)
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