Differential and Integral Equations

On the uniqueness of weak solutions of the two-dimensional primitive equations

D. Bresch, F. Guillén-González, N. Masmoudi, and M. A. Rodríguez-Bellido

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Abstract

The uniqueness of weak solutions of the primitive equations with Dirichlet boundary conditions at the bottom is an open problem even in the two dimensional case. The aim of this paper is to prove the uniqueness of weak solutions when we replace the Dirichlet boundary condition at the bottom by a friction condition. With this boundary condition at the bottom, we establish an additional regularity result for the vertical derivative of the horizontal velocity which allows us to conclude the uniqueness of weak solutions.

Article information

Source
Differential Integral Equations, Volume 16, Number 1 (2003), 77-94.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060697

Mathematical Reviews number (MathSciNet)
MR1948873

Zentralblatt MATH identifier
1042.35042

Subjects
Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10]
Secondary: 76D05: Navier-Stokes equations [See also 35Q30] 86A05: Hydrology, hydrography, oceanography [See also 76Bxx, 76E20, 76Q05, 76Rxx, 76U05]

Citation

Bresch, D.; Guillén-González, F.; Masmoudi, N.; Rodríguez-Bellido, M. A. On the uniqueness of weak solutions of the two-dimensional primitive equations. Differential Integral Equations 16 (2003), no. 1, 77--94. https://projecteuclid.org/euclid.die/1356060697


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