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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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

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

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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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