Spectral transverse instability of solitary waves in Korteweg fluids

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:361

Article

Benzoni-Gavage, S.

关键词: Hamiltonian structure;    Capillarity;    Soliton;    Orbital stability;    Linearized stability;    Evans function;   

DOI  :  10.1016/j.jmaa.2009.07.023

来源: Elsevier

【 摘 要 】

The motion of Korteweg fluids is governed by the Euler-Korteweg model, which admits planar solitary waves for nonmonotone pressure laws such as the van der Waals law below critical temperature. In an earlier work with Danchin, Descombes and Jamet, it was shown by variational arguments and numerical computations that some of these solitary waves are stable in one space dimension. The purpose here is to study their stability with respect to transverse perturbations in several space dimensions. By Evans functions techniques and Rouche's theorem. it is shown that transverse perturbations of large wave length always destabilize solitary waves in the Euler-Korteweg model, whereas energy estimates show that perturbations of short wave length tend to stabilize them. (c) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free