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2013•Boundary Value ProblemsOpen access

Nonlocal Navier-Stokes problem with a small parameter

Veli Shakhmurov

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Abstract

Initial nonlocal boundary value problems for a Navier-Stokes equation with a small parameter is considered. The uniform maximal regularity properties of the corresponding stationary Stokes operator, well-posedness of a nonstationary Stokes problem and the existence, uniqueness and uniformly estimates for the solution of the Navier-Stokes problem are established. MSC:35Q30, 76D05, 34G10, 35J25.

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Initial nonlocal boundary value problems for a Navier-Stokes equation with a small parameter is considered. The uniform maximal regularity properties of the corresponding stationary Stokes operator, well-posedness of a nonstationary Stokes problem and the existence, uniqueness and uniformly estimates for the solution of the Navier-Stokes problem are established. MSC:35Q30, 76D05, 34G10, 35J25.

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Available abstract

Initial nonlocal boundary value problems for a Navier-Stokes equation with a small parameter is considered. The uniform maximal regularity properties of the corresponding stationary Stokes operator, well-posedness of a nonstationary Stokes problem and the existence, uniqueness and uniformly estimates for the solution of the Navier-Stokes problem are established. MSC:35Q30, 76D05, 34G10, 35J25.

Key concepts: Mathematics, Uniqueness, Mathematical analysis, Navier–Stokes equations, Boundary value problem, Non-dimensionalization and scaling of the Navier–Stokes equations, Stokes' law, Partial differential equation

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