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

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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.

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Funding

The work was carried out at the Far Eastern Center for Mathematical Research with financial support from the Ministry of Science and Higher Education of the Russian Federation as part of the implementation of the program for the development of regional scientific and educational mathematical centers under agreement no. 075-02-2023-946.

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Authors and Affiliations

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

    E. V. Amosova

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

    E. V. Amosova

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  1. E. V. Amosova
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Correspondence to E. V. Amosova.

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Translated by V. Potapchouck

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Amosova, E.V. Regularity of the Pressure Function for Weak Solutions of the Nonstationary Navier–Stokes Equations. Diff Equat 59, 1199–1215 (2023). https://doi.org/10.1134/S0012266123090069

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  • DOI: https://doi.org/10.1134/S0012266123090069

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