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Papers by fabien marchand

Research paper thumbnail of Propagation of Sobolev regularity for the critical dissipative quasi-geostrophic equation

Asymptotic Analysis, 2006

Research paper thumbnail of Weak–strong uniqueness criteria for the critical quasi-geostrophic equation

Physica D: Nonlinear Phenomena, 2008

We give two weak-strong uniqueness results for the weak solutions to the critical dissipative qua... more We give two weak-strong uniqueness results for the weak solutions to the critical dissipative quasi-geostrophic equation when the initial data belongs toḢ −1/2. The first one shows that we can construct a uniqueḢ −1/2-solution when the initial data belongs moreover to L ∞ with a small L ∞ norm. The other one gives the uniqueness of aḢ −1/2-solution which belongs to C([0, T), CM O).

Research paper thumbnail of Remarques sur l'unicité pour le système de Navier–Stokes tridimensionnel

Comptes Rendus Mathematique, 2007

Nous donnons un résultat d'unicité pour le système de Navier-Stokes tridimensionnel ; la classe d... more Nous donnons un résultat d'unicité pour le système de Navier-Stokes tridimensionnel ; la classe d'unicité considérée est L 2 ((0, T),Ḣ 1/2) ∩ C([0, T), M 1/2) où M 1/2 est l'espace des multiplicateurs ponctuels deḢ 1/2 dansḢ −1/2. Nous donnons aussi une preuve trés simple de l'unicité des solutions C([0, T), L 3). Pour citer cet article : F.

Research paper thumbnail of Existence and Regularity of Weak Solutions to the Quasi-Geostrophic Equations in the Spaces L p or <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow></mrow><annotation encoding="application/x-tex"></annotation></semantics></math></span><span class="katex-html" aria-hidden="true"></span></span>\dot{H}^{-1/2}$$

Communications in Mathematical Physics, 2007

Research paper thumbnail of Solutions auto-similaires non radiales pour l'équation quasi-géostrophique dissipative critique

Comptes Rendus Mathematique, 2005

We prove the existence of self-similar solutions for the critical dissipative quasi-geostrophic e... more We prove the existence of self-similar solutions for the critical dissipative quasi-geostrophic equation by using the formalism of mild solutions in a space close to L∞. To cite this article: F. Marchand, P.G. Lemarié-Rieusset, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

Research paper thumbnail of Propagation of Sobolev regularity for the critical dissipative quasi-geostrophic equation

Asymptotic Analysis, 2006

Research paper thumbnail of Weak–strong uniqueness criteria for the critical quasi-geostrophic equation

Physica D: Nonlinear Phenomena, 2008

We give two weak-strong uniqueness results for the weak solutions to the critical dissipative qua... more We give two weak-strong uniqueness results for the weak solutions to the critical dissipative quasi-geostrophic equation when the initial data belongs toḢ −1/2. The first one shows that we can construct a uniqueḢ −1/2-solution when the initial data belongs moreover to L ∞ with a small L ∞ norm. The other one gives the uniqueness of aḢ −1/2-solution which belongs to C([0, T), CM O).

Research paper thumbnail of Remarques sur l'unicité pour le système de Navier–Stokes tridimensionnel

Comptes Rendus Mathematique, 2007

Nous donnons un résultat d'unicité pour le système de Navier-Stokes tridimensionnel ; la classe d... more Nous donnons un résultat d'unicité pour le système de Navier-Stokes tridimensionnel ; la classe d'unicité considérée est L 2 ((0, T),Ḣ 1/2) ∩ C([0, T), M 1/2) où M 1/2 est l'espace des multiplicateurs ponctuels deḢ 1/2 dansḢ −1/2. Nous donnons aussi une preuve trés simple de l'unicité des solutions C([0, T), L 3). Pour citer cet article : F.

Research paper thumbnail of Existence and Regularity of Weak Solutions to the Quasi-Geostrophic Equations in the Spaces L p or <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow></mrow><annotation encoding="application/x-tex"></annotation></semantics></math></span><span class="katex-html" aria-hidden="true"></span></span>\dot{H}^{-1/2}$$

Communications in Mathematical Physics, 2007

Research paper thumbnail of Solutions auto-similaires non radiales pour l'équation quasi-géostrophique dissipative critique

Comptes Rendus Mathematique, 2005

We prove the existence of self-similar solutions for the critical dissipative quasi-geostrophic e... more We prove the existence of self-similar solutions for the critical dissipative quasi-geostrophic equation by using the formalism of mild solutions in a space close to L∞. To cite this article: F. Marchand, P.G. Lemarié-Rieusset, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

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