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 study the regularity and local energy equation of the weak solutions for nonhomogeneous incompressible ideal magnetohydrodynamics system.The conditions given on the regularity of solutions guarantee t...In this paper,we study the regularity and local energy equation of the weak solutions for nonhomogeneous incompressible ideal magnetohydrodynamics system.The conditions given on the regularity of solutions guarantee the energy to be conserved.The main method we have employed relies on the commutator estimates.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.
基金the National Natural Science Foundation of China(11871305,11901346)。
文摘In this paper,we study the regularity and local energy equation of the weak solutions for nonhomogeneous incompressible ideal magnetohydrodynamics system.The conditions given on the regularity of solutions guarantee the energy to be conserved.The main method we have employed relies on the commutator estimates.
