Differential and Integral Equations

A simple proof of global solvability of 2-D Navier-Stokes equations in unbounded domains

B.P.W. Fernando, S.S. Sritharan, and M. Xu

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Abstract

In this paper we provide an elementary proof of the classical result of J.L. Lions and G. Prodi on the global unique solvability of two-dimensional Navier-Stokes equations that avoids compact embedding and strong convergence. The method applies to unbounded domains without special treatment. The essential idea is to utilize the local monotonicity of the sum of the Stokes operator and the inertia term. This method was first discovered in the context of stochastic Navier-Stokes equations by J.L. Menaldi and S.S. Sritharan.

Article information

Source
Differential Integral Equations, Volume 23, Number 3/4 (2010), 223-235.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356019315

Mathematical Reviews number (MathSciNet)
MR2588473

Zentralblatt MATH identifier
1240.35383

Subjects
Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 76D05: Navier-Stokes equations [See also 35Q30]

Citation

Fernando, B.P.W.; Sritharan, S.S.; Xu, M. A simple proof of global solvability of 2-D Navier-Stokes equations in unbounded domains. Differential Integral Equations 23 (2010), no. 3/4, 223--235. https://projecteuclid.org/euclid.die/1356019315


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