Les théorèmes de Leray et de Fujita-Kato pour le système de Boussinesq partiellement visqueux
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Publication:3614870
DOI10.24033/bsmf.2557zbMath1162.35063arXiv0806.4083OpenAlexW2489456039MaRDI QIDQ3614870
Publication date: 16 March 2009
Published in: Bulletin de la Société mathématique de France (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0806.4083
Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10)
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Cites Work
- Strong \(L^ p\)-solutions of the Navier-Stokes equation in \(R^ m\), with applications to weak solutions
- On the global well-posedness of the two-dimensional Boussinesq system with a zero diffusivity
- Hydrodynamics in Besov spaces
- Uniqueness theorems for the three dimensional Navier-Stokes system
- Transport equations due to the non-Lipschitzian vector fields and fluid mechanics
- Global well-posedness of the viscous Boussinesq equations
- Flows of non-Lipschitzian vector fields and Navier-Stokes equations
- On the Navier-Stokes initial value problem. I
- On the uniqueness in critical spaces for compressible Navier-Stokes equations
- Estimates in Besov spaces for transport and transport-diffusion equations with almost Lipschitz coefficients
- Global regularity for the 2D Boussinesq equations with partial viscosity terms
- On the Boussinesq Flow with Nondecaying Initial Data
- UNIFORM ESTIMATES FOR TRANSPORT-DIFFUSION EQUATIONS
- Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires
- Remarques sur l’Existence Globale Pour le Système de Navier–Stokes Incompressible
- Density-dependent incompressible viscous fluids in critical spaces
- On Squirt Singularities in Hydrodynamics
- Small-scale structures in Boussinesq convection
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