A Global L -gradient Estimate on Weak Solutions to Nonlinear Stationary Navier-stokes Equations under Mixed Boundary Conditions
نویسنده
چکیده
In this paper, we prove the integrability of the gradient ru to an exponent > 2 near the boundary, u being a weak solution of a nonlinear stationary Navier-Stokes equation under general mixed boundary conditions. As a consequence of this the pressure p belongs to the Campanato space L 2;; (() with := n ?2. Our method of proof relies on an adaption of a technique by Gehring-Giaquinta-Modica (higher integrability by reverse HH older inequality) to cubes which possible intersect a hyperplane.
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