GLOBAL EXISTENCE AND POINTWISE ESTIMATES OF SOLUTIONS TO GENERALIZED KURAMOTO-SIVASHINSKY SYSTEM IN MULTI-DIMENSIONS

doi:10.1007/s10473-019-0115-8

Abstract

Abstract: The Cauchy problem of the generalized Kuramoto-Sivashinsky equation in multi-dimensions (n ≥ 3) is considered. Based on Green's function method, some ingenious energy estimates are given. Then the global existence and pointwise convergence rates of the classical solutions are established. Furthermore, the L^p convergence rate of the solution is obtained.

Key words: Kuramoto-Sivashinsky equation, global existence, pointwise estimates, Green's function method, energy method

Yingshu ZHANG, Lang LI, Shaomei FANG. GLOBAL EXISTENCE AND POINTWISE ESTIMATES OF SOLUTIONS TO GENERALIZED KURAMOTO-SIVASHINSKY SYSTEM IN MULTI-DIMENSIONS[J].Acta mathematica scientia,Series B, 2019, 39(1): 180-194.

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