L^p -estimates of the Stokes resolvent with nonhomogeneous boundary conditions in 3D exterior domains - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2020

L^p -estimates of the Stokes resolvent with nonhomogeneous boundary conditions in 3D exterior domains

Abstract

The article deals with the homogeneous Stokes resolvent system in a 3D exterior domain, under inhomogeneous Dirichet boundary conditions. Solutions to this boundary value problem are estimated in L^p-norms, with the bounds in these estimates depending on the absolute value of the resolvent parameter λ in an explicit way. Two types of boundary data are considered, that is, L^p-and W^{2−1/p, p}-data. It is shown in particular that the L^p-norm of the velocity outside a vicinity of the boundary, after subtraction of the gradient of a certain harmonic function, is bounded by a constant times |λ| \| b\|p. This estimate carries over to the Oseen resolvent system , leading to a result which has applications in the theory of spatial asymptotics of solutions to the 3D time-dependent Navier-Stokes system with Oseen term.
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Dates and versions

hal-02925916 , version 1 (31-08-2020)

Identifiers

  • HAL Id : hal-02925916 , version 1

Cite

Paul Deuring. L^p -estimates of the Stokes resolvent with nonhomogeneous boundary conditions in 3D exterior domains. 2020. ⟨hal-02925916⟩
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