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1998 Local regularity of non-resonant nonlinear wave equations
Kimitoshi Tsutaya
Differential Integral Equations 11(2): 279-292 (1998).

Abstract

We study the problem of minimal regularity required to ensure local well-posedness for systems of nonlinear wave equations with different propagation speeds in three space dimensions $$ \begin{align} (\partial_t^2 -C_1^2\Delta)u &= F(u,v,\partial u,\partial v), \\ (\partial_t^2 -C_2^2\Delta)v &= G(u,v,\partial u,\partial v). \end{align} $$ We prove that if $C_2 > C_1$ and $F$, $G$ have the form $\p u \cdot v$, then the problem is well-posed in $H^1$. Our proof is based on the same type of space-time estimates as those of Klainerman and Machedon.

Citation

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Kimitoshi Tsutaya. "Local regularity of non-resonant nonlinear wave equations." Differential Integral Equations 11 (2) 279 - 292, 1998.

Information

Published: 1998
First available in Project Euclid: 30 April 2013

zbMATH: 1004.35093
MathSciNet: MR1741846

Subjects:
Primary: 35L70

Rights: Copyright © 1998 Khayyam Publishing, Inc.

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Vol.11 • No. 2 • 1998
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