科研之友
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摘要
We address the global regularity of solutions of the Navier-Stokes equations in a domain with periodic boundary conditions. We prove that the solutions are smooth under some structural conditions and some natural conditions on the horizontal derivatives of the horizontal components of the velocity and the derivative in the vertical direction. The obtained conditions admit data whose vertical average is large in BMO (-1). We emphasize that unlike previously known results, our data do not need to oscillate in any direction. Also, the results allow non-zero force and lead to solutions which do not decay in time.
- 出版日期2014-6
