A Navier–Stokes-Type Problem with High-Order Elliptic Operator and Applications

Maria Alessandra Ragusa and Veli B. Shakhmurov
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Maria Alessandra Ragusa: Dipartimento di Matematica e Informatica, Universitá degli Studi di Catania, 95125 Catania, Italy
Veli B. Shakhmurov: Antalya Bilim University, Çiplakli Mah. Farabi Cad. 23 Dosemealti, 07190 Antalya, Turkey

Mathematics, 2020, vol. 8, issue 12, 1-23

Abstract: The existence, uniqueness and uniformly L p estimates for solutions of a high-order abstract Navier–Stokes problem on half space are derived. The equation involves an abstract operator in a Banach space E and small parameters. Since the Banach space E is arbitrary and A is a possible linear operator, by choosing spaces E and operators A , the existence, uniqueness and L p estimates of solutions for numerous classes of Navier–Stokes type problems are obtained. In application, the existence, uniqueness and uniformly L p estimates for the solution of the Wentzell–Robin-type mixed problem for the Navier–Stokes equation and mixed problem for degenerate Navier–Stokes equations are established.

Keywords: stokes systems; Navier–Stokes equations; differential equations with small parameters; semigroups of operators; differential-operator equations; maximal L p regularity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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