可压缩Navier-Stokes-Korteweg系统解具有扩散波性质和平滑效应的时间衰减估计

Pub Date : 2019-05-31 DOI:10.1619/fesi.64.163
Takayuki Kobayashi, Kazuyuki Tsuda
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引用次数: 2

摘要

研究了可压缩Navier-Stokes-Korteweg系统解的时间衰减估计。对于线性化问题,导出了初始数据具有扩散波性质的衰减估计。作为应用,给出了非线性问题解的时间衰减估计。与可压缩的Navier-Stokes系统相比,由于Korteweg张量的平滑作用,线性系统初始数据的规律性较低,且与解的导数阶数无关。此外,对于非线性系统的扩散波性质,用比可压缩Navier-Stokes系统的正则性更低的初始数据得到。
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Time Decay Estimate with Diffusion Wave Property and Smoothing Effect for Solutions to the Compressible Navier-Stokes-Korteweg System
Time decay estimate of solutions to the compressible Navier-Stokes-Korteweg system is studied. Concerning the linearized problem, the decay estimate with diffusion wave property for an initial data is derived. As an application, the time decay estimate of solutions to the nonlinear problem is given. In contrast to the compressible Navier-Stokes system, for linear system regularities of the initial data are lower and independent of the order of derivative of solutions owing to smoothing effect from the Korteweg tensor. Furthermore, for the nonlinear system diffusion wave property is obtained with an initial data having lower regularity than that of study of the compressible Navier-Stokes system.
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