Preprint 2002-042

Weakly Stable Multi-d Shocks

Jean-Francois Coulombel

Abstract: We study the linear stability of multidimensional shock waves for systems of conservation laws in the case where Majda's uniform stability condition is violated. The linearized problem is attacked using the "good unknown" of Alinhac. We prove an energy estimate and show that the solutions to the linearized problem have singularities localized along bicharacteristic curves originating from the boundary. The application to isentropic gas dynamics is detailed.

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Jean-Francois Coulombel, <>
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<> July 15 2002.

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