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The time periodic problem of the Navier–Stokes equations in a bounded domain with moving boundary
Nonlinear Analysis: Real World Applications ( IF 2 ) Pub Date : 2021-04-21 , DOI: 10.1016/j.nonrwa.2021.103339 Reinhard Farwig , Hideo Kozono , Kazuyuki Tsuda , David Wegmann
中文翻译:
带有运动边界的有界域中Navier–Stokes方程的时间周期问题
更新日期:2021-04-22
Nonlinear Analysis: Real World Applications ( IF 2 ) Pub Date : 2021-04-21 , DOI: 10.1016/j.nonrwa.2021.103339 Reinhard Farwig , Hideo Kozono , Kazuyuki Tsuda , David Wegmann
The time periodic problem of the Navier–Stokes equations on a non-cylindrical space–time domain is studied. Motivated by a recent result by Saal (2006) on maximal regularity for this kind of system we construct time periodic solutions in -spaces provided the bounded domain moves periodically with small amplitude and the given periodic external force is small. The proof is based on new decay estimates for the solution operator of parabolic evolution equations corresponding to the non-cylindrical space–time domain problem.
中文翻译:
带有运动边界的有界域中Navier–Stokes方程的时间周期问题
研究了非圆柱时空域上Navier-Stokes方程的时间周期问题。根据Saal(2006)最近针对此类系统的最大规则性的结果,我们构造了时间周期解如果有界域周期性地以小幅度运动并且给定的周期性外力很小,则该空间是有限的。证明基于抛物线发展方程解运算符的新的衰减估计,该方程对应于非圆柱的时空问题。