Local well-posedness of perturbed Navier-Stokes system around Landau solutions

Abstract

<p style='text-indent:20px;'>For the incompressible Navier-Stokes system, when initial data are uniformly locally square integral, the local existence of solutions has been obtained. In this paper, we consider perturbed system and show that perturbed solutions of Landau solutions to the Navier-Stokes system exist locally under <inline-formula><tex-math id="M1">$ L^q_{\text{uloc}} $</tex-math></inline-formula>-perturbations, <inline-formula><tex-math id="M2">$ q\geq 2 $</tex-math></inline-formula>. Furthermore, when <inline-formula><tex-math id="M3">$ q\geq 3, $</tex-math></inline-formula> the solution is well-posed. Precisely, we give the explicit formula of the pressure term.</p>