In this paper,we investigate the large time behavior of solutions to the three dimensional generalized Hall-magnetohydrodynamics(Hall-MHD)system in the spacesχ^(s)(R^(3)).We obtain that the temporal decay rate is‖(u...In this paper,we investigate the large time behavior of solutions to the three dimensional generalized Hall-magnetohydrodynamics(Hall-MHD)system in the spacesχ^(s)(R^(3)).We obtain that the temporal decay rate is‖(u,b)(t)‖χ^(1−2α)+‖(u,b)(t)‖χ^(1−2β)+‖(u,b)(t)‖χ^(2−2α)+‖(u,b)(t)‖χ^(2−2β)≤(1 t)^(-(5-4max{α,β}/4max{α,β})with 1/2≤α,β≤1 for the small global solution by using Fourier splitting method.The parametersαandβare the fractional dissipations corresponding to the velocity and magnetic field,respectively.展开更多
In this paper, we are concerned with the Cauchy problem of the full compressible Hall-magnetohydrodynamic equations in three-dimensional whole space. By the energy method, global existence of a unique strong solution ...In this paper, we are concerned with the Cauchy problem of the full compressible Hall-magnetohydrodynamic equations in three-dimensional whole space. By the energy method, global existence of a unique strong solution is established. If further that the L1-norm of the perturbation is bounded, we prove the decay rates in time of the solution and its first-order derivatives in L2-norm via some Lp-Lq estimates by the linearized operator.展开更多
基金Supported by the National Natural Science Foundation of China(11871305)
文摘In this paper,we investigate the large time behavior of solutions to the three dimensional generalized Hall-magnetohydrodynamics(Hall-MHD)system in the spacesχ^(s)(R^(3)).We obtain that the temporal decay rate is‖(u,b)(t)‖χ^(1−2α)+‖(u,b)(t)‖χ^(1−2β)+‖(u,b)(t)‖χ^(2−2α)+‖(u,b)(t)‖χ^(2−2β)≤(1 t)^(-(5-4max{α,β}/4max{α,β})with 1/2≤α,β≤1 for the small global solution by using Fourier splitting method.The parametersαandβare the fractional dissipations corresponding to the velocity and magnetic field,respectively.
文摘In this paper, we are concerned with the Cauchy problem of the full compressible Hall-magnetohydrodynamic equations in three-dimensional whole space. By the energy method, global existence of a unique strong solution is established. If further that the L1-norm of the perturbation is bounded, we prove the decay rates in time of the solution and its first-order derivatives in L2-norm via some Lp-Lq estimates by the linearized operator.
