A maximum modulus estimate for solutions of the Navier-Stokes system in domains of polyhedral type

Mixed boundary value problems for the Navier-Stokes system in polyhedral domains

Mixed boundary value problems for the Navier-Stokes system in a polyhedral domain are considered. Different boundary conditions (in particular, Dirichlet, Neumann, slip conditions) are prescribed on the faces of a polyhedron. The authors obtain regularity results for weak solutions in weighted (and non-weighted) L_p Sobolev and Hölder spaces.

通过调和压力实现三维Navier-Stokes方程的有限尺度单分量正则性

Finite-Scale One-Component Regularity via Harmonic Pressure for the 3D Navier-Stokes Equations

研究三维不可压缩Navier-Stokes方程适度弱解的有限尺度单分量正则性机制，通过调和压力近似将单分量小性转化为更小尺度的Caffarelli-Kohn-Nirenberg小性，并给出条件性的对数型和幂次型改进。