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Open Access Research

Nonlocal Navier-Stokes problem with a small parameter

Veli B Shakhmurov

Author Affiliations

Department of Mechanical Engineering, Okan University, Akfirat, Tuzla, Istanbul, Turkey

Institute of Mathematics and Mechanics, Azerbaijan National Akademy of Science, Baku, Azerbaijan

Boundary Value Problems 2013, 2013:107  doi:10.1186/1687-2770-2013-107

Published: 26 April 2013

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 <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/107/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/107/mathml/M1">View MathML</a> estimates for the solution of the Navier-Stokes problem are established.

MSC: 35Q30, 76D05, 34G10, 35J25.

Keywords:
Stokes operators; Navier-Stokes equations; differential equations with small parameters; semigroups of operators; boundary value problems; differential-operator equations; maximal <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/107/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/107/mathml/M2">View MathML</a> regularity