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Sur la solution à support compact de l’equation d’Euler compressible. (Solutions with compact support of the compressible Euler equation). (French) Zbl 0637.76065
Summary: The Cauchy problem for the compressible Euler equation is discussed with compactly supported initials. To establish the local existence of classical solutions by the aid of the theory of quasilinear symmetric hyperbolic systems, a new symmetrization is introduced which works for initials having compact support or vanishing at infinity. It is further shown that as far as the classical solution is concerned, its support does not change, and that the life span is finite for any solution except for the trivial zero solution.

MSC:
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35Q30 Navier-Stokes equations
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