Global Regularity for a Class of Generalized Magnetohydrodynamic Equations
نویسنده
چکیده
It remains unknown whether or not smooth solutions of the 3D incompressible MHD equations can develop finite-time singularities. One major difficulty is due to the fact that the dissipation given by the Laplacian operator is insufficient to control the nonlinearity and for this reason the 3D MHD equations are sometimes regarded as “supercritical”. This paper presents a global regularity result for the generalized MHD equations with a class of hyperdissipation. This result is inspired by a recent work of Terence Tao on a generalized Navier–Stokes equations (T. Tao, Global regularity for a logarithmically supercritical hyperdissipative Navier–Stokes equations, arXiv: 0906.3070v3 [math.AP] 20 June 2009), but the result for the MHD equations is not completely parallel to that for the Navier–Stokes equations. Besov space techniques are employed to establish the result for the MHD equations. AMS (MOS) Numbers. 76W05, 35Q35, 76D03.
منابع مشابه
Regularity Criteria for the Three-dimensional Magnetohydrodynamic Equations
This paper studies the three-dimensional density-dependent incompressible magnetohydrodynamic equations. First, a regularity criterion is proved which allows the initial density to contain vacuum. Then we establish another blow-up criterion in the Besov space Ḃ0 ∞,2 when the positive initial density is bounded away from zero. Third, we prove a global nonexistence result for initial density with...
متن کاملNote on solution regularity of the generalized magnetohydrodynamic equations with partial dissipation
متن کامل
Global Regularity for the 2D Magneto-Micropolar Equations with Partial Dissipation
Abstract. This paper studies the global existence and regularity of classical solutions to the 2D incompressible magneto-micropolar equations with partial dissipation. The magneto-micropolar equations model the motion of electrically conducting micropolar fluids in the presence of a magnetic field. When there is only partial dissipation, the global regularity problem can be quite difficult. We ...
متن کاملThe Generalized Wave Model Representation of Singular 2-D Systems
M. and M. Abstract: Existence and uniqueness of solution for singular 2-D systems depends on regularity condition. Simple regularity implies regularity and under this assumption, the generalized wave model (GWM) is introduced to cast singular 2-D system of equations as a family of non-singular 1-D models with variable structure.These index dependent models, along with a set of boundary co...
متن کامل