This paper is concerned with a stability problem on perturbations near a physically important steady state solution of the 3D MHD system.We obtain three major results.The first assesses the existence of global solutio...This paper is concerned with a stability problem on perturbations near a physically important steady state solution of the 3D MHD system.We obtain three major results.The first assesses the existence of global solutions with small initial data.Second,we derive the temporal decay estimate of the solution in the L^(2)-norm,where to prove the result,we need to overcome the difficulty caused by the presence of linear terms from perturbation.Finally,the decay rate in L^(2) space for higher order derivatives of the solution is established.展开更多
We establish the global well-posedness of a strong solution to the 3D tropical climate model with damping.We prove that there exists the global and unique solution forα,β,γsatisfying one of the following three cond...We establish the global well-posedness of a strong solution to the 3D tropical climate model with damping.We prove that there exists the global and unique solution forα,β,γsatisfying one of the following three conditions:(1)α,β≥4;(2)7/2≤α<4,β≥(5α+7)/(2α),γ≥7/(2α−5);(3)3<α≤7/2,β,γ≥7/(2α−5).展开更多
基金The second author is supported by the National Natural Science Foundation of China(11471103).
文摘This paper is concerned with a stability problem on perturbations near a physically important steady state solution of the 3D MHD system.We obtain three major results.The first assesses the existence of global solutions with small initial data.Second,we derive the temporal decay estimate of the solution in the L^(2)-norm,where to prove the result,we need to overcome the difficulty caused by the presence of linear terms from perturbation.Finally,the decay rate in L^(2) space for higher order derivatives of the solution is established.
基金The research of Baoquan Yuan was partially supported by the National Natural Science Foundation of China(Grant No.11471103).
文摘We establish the global well-posedness of a strong solution to the 3D tropical climate model with damping.We prove that there exists the global and unique solution forα,β,γsatisfying one of the following three conditions:(1)α,β≥4;(2)7/2≤α<4,β≥(5α+7)/(2α),γ≥7/(2α−5);(3)3<α≤7/2,β,γ≥7/(2α−5).
