Asymptotic Linear Stability of Solitary Water Waves

被引：0
作者：
Robert L. Pego
Shu-Ming Sun
机构：
[1] Carnegie Mellon University,Department of Mathematical Sciences, Center for Nonlinear Analysis
[2] Virginia Polytechnic Institute and State University,Department of Mathematics
来源：
Archive for Rational Mechanics and Analysis | 2016年 / 222卷
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摘要：
We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and above by a free surface under the influence of gravity neglecting surface tension. For sufficiently small amplitude waves, with waveform well-approximated by the well-known sech-squared shape of the KdV soliton, solutions of the linearized equations decay at an exponential rate in an energy norm with exponential weight translated with the wave profile. This holds for all solutions with no component in (that is, symplectically orthogonal to) the two-dimensional neutral-mode space arising from infinitesimal translational and wave-speed variation of solitary waves. We also obtain spectral stability in an unweighted energy norm.
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页码：1161 / 1216
页数：55
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