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Nonlocal abstract Stokes operators and applications
https://doi.org/10.26907/0021-3446-2025-8-69-83
Abstract
In this paper, the Cauchy problem for the stationary and nonstationary nonlocal incompressible abstract Stokes equation is considered. The equation involves a convolution term and an abstract operator in a Banach space E. Existence, uniqueness, and coercive estimates are derived in L p spaces. Different classes of Stokes equations can be obtained by choosing the space E and the linear operator A, which occur in a wide variety of physical systems. As an application of the obtained results, the existence, uniqueness, and L p -maximal regularity properties of solutions to initial value problems for nonlocal degenerate Stokes equations and nonlocal Stokes equations with discontinuous coefficients are established.
About the Author
V. B. Shakhmurov
Antalya Bilim University
Turkey
Turkey
Veli Binnet Shakhmurov
Dosemealti, Antalya, 07190
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Review
For citations:
Shakhmurov V.B. Nonlocal abstract Stokes operators and applications. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 2025;1(8):69-83. (In Russ.) https://doi.org/10.26907/0021-3446-2025-8-69-83
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