We consider suitable weak solutions to the Navier–Stokes equations in time varying domains. We develop Schauder theory for the approximate Stokes equations in time varying domains whose solutions satisfy a uniform localized energy estimate including boundary. Existence of suitable weak solutions in time varying domains follows from compactness in Lebesgue and Sobolev spaces.
|Number of pages||14|
|Journal||Nonlinear Analysis, Theory, Methods and Applications|
|Publication status||Published - 2017 Nov|
Bibliographical noteFunding Information:
The authors would like to express their sincere gratitude to the referee for careful reading and for many helpful comments. Hi Jun Choe has been supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2015R1A5A1009350 ). Yunsoo Jang has been supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. NRF-2016R1D1A1B03935364 ). Minsuk Yang has been supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2016R1C1B2015731 ).
All Science Journal Classification (ASJC) codes
- Applied Mathematics