Existence and regularizing rate estimates of solutions to a generalized magneto-hydrodynamic system in pseudomeasure spaces

DOI10.1007/s10231-010-0184-8zbMath1239.35033OpenAlexW2169628436MaRDI QIDQ415454

Qiao Liu, Ji-Hong Zhao, Shang-bin Cui

Publication date: 8 May 2012

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10231-010-0184-8

zbMATH Keywords

Cauchy problemgeneralized magneto-hydrodynamic systempseudomeasure spaceregularizing ratespatial analyticity

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Magnetohydrodynamics and electrohydrodynamics (76W05)

Related Items (17)

On analyticity rate estimates to the magneto-hydrodynamic equations in Besov-Morrey spaces ⋮ Existence and regularizing rate estimates of mild solutions to a generalized magneto-hydrodynamic system in Q-spaces ⋮ On well-posedness of generalized Hall-magneto-hydrodynamics ⋮ Well-posedness and stability for the generalized incompressible magneto-hydrodynamic equations in critical Fourier-Besov-Morrey spaces ⋮ Existence and analyticity of mild solutions for the 3D rotating Navier-Stokes equations ⋮ Global well-posedness for the generalized magneto-hydrodynamic equations in the critical Fourier-Herz spaces ⋮ Unilateral rigidity from infinity for nonlinear Alfvén waves in ideal magnetohydrodynamics ⋮ Gevrey class regularity and stability for the Debye-H¨uckel system in critical Fourier-Besov-Morrey spaces ⋮ Space-time regularity of the \textit{mild} solutions to the incompressible generalized Navier-Stokes equations with small rough initial data ⋮ Global well-posedness of the generalized incompressible Navier-Stokes equations with large initial data ⋮ Global well-posedness of the generalized magnetohydrodynamic equations ⋮ On weak-strong uniqueness of solutions to the generalized incompressible Navier-Stokes equations ⋮ Well-posedness and decay of solutions to 3D generalized Navier-Stokes equations ⋮ Global existence and Gevrey regularity to the Navier-Stokes-Nernst-Planck-Poisson system in critical Besov-Morrey spaces ⋮ Global well-posedness and decay results to 3D generalized viscous magnetohydrodynamic equations ⋮ Global well-posedness, Gevrey class regularity and large time asymptotics for the dissipative quasi-geostrophic equation in Fourier-Besov spaces ⋮ Space-time regularity for the three dimensional Navier-Stokes and MHD equations

Cites Work

• On the equations of ideal incompressible magneto-hydrodynamics
• Generalized MHD equations.
• Smooth or singular solutions to the Navier-Stokes system?
• Regularity results for weak solutions of the 3D MHD equations.
• Regularizing rate estimates for mild solutions of the incompressible magneto-hydrodynamic system
• On the spatial analyticity of solutions of the Navier-Stokes equations
• On analyticity rate estimates of the solutions to the Navier--Stokes equations in Bessel-potential spaces
• Some mathematical questions related to the mhd equations
• Existence of solutions to the convection problem in a pseudomeasure-type space
• Self-similarity in viscous Boussinesq equations
• Regularity Criteria for the Generalized MHD Equations
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