\(L^p\) and \(W^{1,p}\) regularity of the solution of a steady transport equation

DOI10.1016/j.crma.2010.06.025zbMath1200.35207OpenAlexW1968536606MaRDI QIDQ990242

Vivette Girault, Luc Tartar

Publication date: 6 September 2010

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2010.06.025

zbMATH Keywords

regularizationtransport equationYosida approximation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element methods applied to problems in fluid mechanics (76M10) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Weak solutions to PDEs (35D30) Boltzmann equations (35Q20)

Related Items (7)

Transport equations with inflow boundary conditions ⋮ Solutions in \(H^1\) of the steady transport equation in a bounded polygon with a fully non-homogeneous velocity ⋮ Well-posedness of the scalar and the vector advection-reaction problems in Banach graph spaces ⋮ Well-posedness and H(div)-conforming finite element approximation of a linearised model for inviscid incompressible flow ⋮ Circumventing the lack of dissipation in certain Oldroyd models ⋮ The discrete-dual minimal-residual method (DDMRES) for weak advection-reaction problems in Banach spaces ⋮ Some multiple flow direction algorithms for overland flow on general meshes

Cites Work

• Existence results in Sobolev spaces for a stationary transport equation
• Ordinary differential equations, transport theory and Sobolev spaces
• Analysis of a two-dimensional grade-two fluid model with a tangential boundary condition
• Problèmes aux limites pour les équations aux dérivées partielles du premier ordre à coefficients réels; théorèmes d'approximation; application à l'équation de transport
• Unnamed Item

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