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Open Access Research

Stokes operators with variable coefficients and applications

Veli B Shakhmurov

Author Affiliations

Department of Mechanical Engineering, Okan University, Akfirat, Tuzla, Istanbul, 34959, Turkey

Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku, Azerbaijan

Boundary Value Problems 2014, 2014:86  doi:10.1186/1687-2770-2014-86

Published: 2 May 2014

Abstract

The stationary and instationary Stokes problems with variable coefficients in abstract <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/86/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/86/mathml/M2">View MathML</a> spaces are considered. The problems contain abstract operators and nonlocal boundary conditions. The well-posedness of these problems is derived.

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

Keywords:
Stokes systems; Navier-Stokes equations; abstract differential equations with variable coefficients; semigroups of operators; boundary value problems; maximal <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/86/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/86/mathml/M2">View MathML</a> regularity