Global regularity to the 3D incompressible MHD equations

[摘要] In this paper, we prove the global regularity to the 3D nonhomogeneous incompressible magnetohydrodynamic equations. Let (sic)(0), m(0) and H-0 be the initial density, momentum and magnetic field, respectively. We establish a unique strong solution on R-3 x (0, T) for any 0 < T < infinity under the assumption that the viscosity coefficient mu > 0 is sufficiently large, or parallel to vertical bar m(0)vertical bar(2)/(sic)(0)parallel to(2)(L1) + parallel to H-0 parallel to(2)(L2) or parallel to del u(0)parallel to(2)(L2) + parallel to H-0 parallel to(2)(H1) is small enough. Moreover, if the given data are more regular and satisfy an additional compatibility condition for the existence of strong solution, then we show that the strong solution is indeed a classical one. Moreover, the weak strong uniqueness of solutions is also obtained, which generalizes the result in [13] to the case of vacuum. (C) 2015 Elsevier Inc. All rights reserved.

[发布日期] 2015-12-15

[关键词] Incompressible MHD equations;Global regularity;Vacuum