We study boundary regularity of weak solutions of the Navier-Stokes equations in the half-space in dimension n ≥ 3. We prove that a weak solution u which is locally in the class Lp,q with 2/p + n/q = 1, q > n near boundary is Hölder continuous up to the boundary. Our main tool is a pointwise estimate for the fundamental solution of the Stokes system, which is of independent interest.
All Science Journal Classification (ASJC) codes
- Applied Mathematics