Quasi-Maximum Modulus Principle for the Stokes Equations
详细信息 查看全文
- 作者：Tongkeun Chang ; Hi Jun Choe
- 关键词：Nonstationary Stokes equation ; maximum modulus principle ; normal velocity ; log ; Dini continuous
- 刊名：Journal of Mathematical Fluid Mechanics
- 出版年：2017
- 出版时间：March 2017
- 年：2017
- 卷：19
- 期：1
- 页码：135-149
- 全文大小：
- 刊物类别：Physics and Astronomy
- 刊物主题：Fluid- and Aerodynamics; Mathematical Methods in Physics; Classical and Continuum Physics;
- 出版者：Springer International Publishing
- ISSN：1422-6952
- 卷排序：19
文摘
In this paper, we extend the maximum modulus estimate of the solutions of the nonstationary Stokes equations in the bounded C2 cylinders for the space variables in Chang and Choe (J Differ Equ 254(7):2682–2704, 2013) to time estimate. We show that if the boundary data is \({L^{\infty}}\) and the normal part of the boundary data has log-Dini continuity with respect to the time, then the velocity is bounded. We emphasize that there is no continuity assumption on space variables in the new maximum modulus estimate. This completes the maximum modulus estimate.