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Navier–Stokes Problems with Small Parameters in Half-Space and Application

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Abstract

We derive the existence, uniqueness, and uniform \( L^{p} \) estimates for the abstract Navier–Stokes problem with small parameters in half-space. The equation involves small parameters and an abstract operator in a Banach space \( E \). Hence, we obtain the singular perturbation property for the Stokes operator depending on a parameter. We can obtain the various classes of Navier–Stokes equations by choosing \( E \) and the linear operators \( A \). These classes occur in a wide variety of physical systems. As application we establish the existence, uniqueness, and uniform \( L^{p} \) estimates for the solution of the mixed problems for infinitely many Navier–Stokes equations and nonlocal mixed problems for the high order Navier–Stokes equations.

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Authors and Affiliations

  1. Department of Industrial Engineering, Antalya Bilim University, Antalya, Turkey

    V. B Shakhmurov

  2. Center of Analytical-Information Resource, Azerbaijan State Economic University, Baku, Azerbaijan

    V. B Shakhmurov

Authors
  1. V. B Shakhmurov
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Correspondence to V. B Shakhmurov.

Additional information

Translated from Sibirskii Matematicheskii Zhurnal, 2023, Vol. 64, No. 1, pp. 213–234. https://doi.org/10.33048/smzh.2023.64.118

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Shakhmurov, V.B. Navier–Stokes Problems with Small Parameters in Half-Space and Application. Sib Math J 64, 181–201 (2023). https://doi.org/10.1134/S0037446623010184

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  • DOI: https://doi.org/10.1134/S0037446623010184

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