We consider the problem of regularization by noises for the three-dimensional magnetohydrodynamical(3D MHD) equations. It is shown that in a suitable scaling limit, the multiplicative noise of transport type gives ris...We consider the problem of regularization by noises for the three-dimensional magnetohydrodynamical(3D MHD) equations. It is shown that in a suitable scaling limit, the multiplicative noise of transport type gives rise to bounds on the vorticity fields of the fluid velocity and magnetic fields. As a result, if the noise intensity is big enough, then the stochastic 3D MHD equations admit a pathwise unique global solution for large initial data with high probability.展开更多
Let （Zt）t≥o be a one-dimensional symmetric α-stable process with α ∈ （0, 2）, and let a be a bounded （from above and from below） and 1/（α V 1）- Holder continuous function on R. Consider the stochastic diff...Let （Zt）t≥o be a one-dimensional symmetric α-stable process with α ∈ （0, 2）, and let a be a bounded （from above and from below） and 1/（α V 1）- Holder continuous function on R. Consider the stochastic differential equation dXt = σ（Xt-）dZt, which admits a unique strong solution. By using the splitting technique and the coupling method, we derive the HSlder continuity of the associated semigroup.展开更多
基金supported by the National Key R&D Program of China (Grant No.2020YFA0712700)National Natural Science Foundation of China (Grant Nos. 11931004 and 12090014)+1 种基金the Youth Innovation Promotion AssociationChinese Academy of Sciences (Grant No. Y2021002)。
文摘We consider the problem of regularization by noises for the three-dimensional magnetohydrodynamical(3D MHD) equations. It is shown that in a suitable scaling limit, the multiplicative noise of transport type gives rise to bounds on the vorticity fields of the fluid velocity and magnetic fields. As a result, if the noise intensity is big enough, then the stochastic 3D MHD equations admit a pathwise unique global solution for large initial data with high probability.
基金The authors were indebted to the referees for their helpful comments and careful corrections. The first author＇s work was supported by the Key Laboratory of Random Complex Structures and Data Sciences, Chinese Academy of Sciences （2008DP173182）, the National Natural Science Foundation of China （Grant No. 11571347）, and Academy of Mathematics and Systems Science （Y129161ZZ1）. The second author＇s work was supported by the National Natural Science Foundation of China （Grant Nos. 11201073 and 11522106）, the National Science Foundation of Fujian Province （2015J01003）, and the Program for Nonlinear Analysis and Its Applications （IRTL1206）.
文摘Let （Zt）t≥o be a one-dimensional symmetric α-stable process with α ∈ （0, 2）, and let a be a bounded （from above and from below） and 1/（α V 1）- Holder continuous function on R. Consider the stochastic differential equation dXt = σ（Xt-）dZt, which admits a unique strong solution. By using the splitting technique and the coupling method, we derive the HSlder continuity of the associated semigroup.
