Estimates of anisotropic Sobolev spaces with mixed norms for the Stokes system in a half-space

2013/08/07 by Tongkeun Chang, Chang, Tongkeun, Kyungkeun Kang +1 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1308.1457

arxiv created 2013/08/07 · arxiv updated 2013/08/08

Abstract

We are concerned with the non-stationary Stokes system with non-homogeneous external force and non-zero initial data in \mathbb Rⁿ₊ × (0,T). We obtain new estimates of solutions including pressure in terms of mixed anisotropic Sobolev spaces. As an application, some anisotropic Sobolev estimates are presented for weak solutions of the Navier-Stokes equations in a half-space in dimension three.

Cited by

• Remarks on the maximal regularity for parabolic boundary value problems with inhomogeneous data

Related

• Mixed-norm L_p-estimates for non-stationary Stokes systems with singular VMO coefficients and applications
• Interior and boundary mixed norm derivative estimates for nonstationary Stokes equations
• Potentials and transmission problems in weighted Sobolev spaces for anisotropic Stokes and Navier-Stokes systems with L_∞ strongly elliptic coefficient tensor
• Weighted estimates for the Stokes semigroup in the half-space
• Navier-Stokes problems in half space with parameters