Local in time existence of solution of the Navier-Stokes equations with various types of boundary conditions

摘要

In this paper we deal with the two-dimensional Navier-Stokes system with three types of boundary conditions, including the so called “do-nothing” boundary condition. We prove the local in time existence and uniqueness of a solution for the initial velocity, which can belong to a class of functions that can be at least a little stronger than L2(Ω)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${varvec{L}}^2(Omega )$$end{document}.