On the Solvability of a Boundary Value Problem for a Two-Dimensional System of Navier–Stokes Equations in a Truncated Cone

Muvasharkhan Jenaliyev, Madi Yergaliyev

2023

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DOI 10.1134/s199508022308022x
Data confidence 70 medium
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Abstract

Abstract The paper is devoted to the problems of solvability in Sobolev classes of the boundary value problem for a two-dimensional system of Navier–Stokes equations in a non-cylindrical domain represented by a truncated cone. A special basis consisting of eigenfunctions of one spectral problem is constructed. Using the methods of a priori estimates and Faedo–Galerkin, we prove theorems about the existence and uniqueness of the solution to the boundary value problem under consideration, and its regularity with increasing the smoothness of the given functions.