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

By Didier Bresch, F. Guillén-González, Nader Masmoudi, María Ángeles Rodríguez-Bellido. Differential and Integral Equations, 2003

67 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/8c7e33137dca388846e88f1b1f4e157649346c3b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Davdi Gerard-Varet
2. Nader Masmoudi
3. Vlad Vicol

In Control and Systems Engineering

1. Nader Masmoudi
2. Vlad Vicol
3. Davdi Gerard-Varet
4. Jacob Bedrossian
5. Yasunori Maekawa
6. Igor Kukavica
7. Pierre Germain

In Numerical Analysis

1. Davdi Gerard-Varet
2. Nader Masmoudi
3. Vlad Vicol
4. Peter Constantin

Citations in the corpus

• Well-posedness of the hydrostatic Navier–Stokes equations (2018, background): “1) is called the two-dimensional primitive equations, and has been widely studied, in various geometries and under various boundary conditions [4, 3, 40].”