Regularity of the Pressure Function for Weak Solutions of the Nonstationary Navier–Stokes Equations-Reference-Cited by-同舟云学术

Regularity of the Pressure Function for Weak Solutions of the Nonstationary Navier–Stokes Equations

Published:2023-12-15 Issue:9 Volume:59 Page:1205-1221
ISSN:0374-0641
Container-title:Дифференциальные уравнения
language:
Short-container-title:Differencialʹnye uravneniâ

Author:

Amosova E. V.¹²

Affiliation:

1. Institute of Applied Mathematics, Far East Branch, Russian Academy of Sciences, Vladivostok, 690041, Russia

2. Far Eastern Federal University, Vladivostok, 690090, Russia

Abstract

We study the nonstationary system of Navier–Stokes equations for an incompressible fluid. Based on a regularized problem that takes into account the relaxation of the velocity field into a solenoidal field, the existence of a pressure function almost everywhere in the domain under consideration for solutions in the Hopf class is substantiated. Using the proposed regularization, we prove the existence of more regular weak solutions of the original problem without smallness restrictions on the original data. A uniqueness theorem is proven in the two-dimensional case

Publisher

The Russian Academy of Sciences

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