The Cauchy problem for the 3D incompressible magneto-hydrodynamics equations in crit- cal spaces is considered. We first prove the global well-posedness of mild solution for the system in some time dependent spaces. F...The Cauchy problem for the 3D incompressible magneto-hydrodynamics equations in crit- cal spaces is considered. We first prove the global well-posedness of mild solution for the system in some time dependent spaces. Furthermore, we obtain analyticity of the solution.展开更多
We prove two new regularity criteria for the 3D incompressible Navier-Stokes equations in a bounded domain. Our results also hold for the 3D Boussinesq system with zero heat conductivity.
基金Supported by Research supported by the National Natural Science Foundation of China(Grant Nos.11501332,11771043,11371221)the Natural Science Foundation of Shandong Province(Grant No.ZR2015AL007)+4 种基金China Postdoctoral Science Foundation funded project(Grant No.2014M561893)Postdoctoral innovation fund of Shandong Province(Grant No.201502015)the Open Fund of State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin,China Institute of Water Resources and Hydropower Research Fund(Grant No.IWHR-SKL-201407)the Specialized Research Foundation for the Doctoral Program of Higher Education of China(Grant No.20123705110001)Young Scholars Research Fund of Shandong University of Technology
文摘The Cauchy problem for the 3D incompressible magneto-hydrodynamics equations in crit- cal spaces is considered. We first prove the global well-posedness of mild solution for the system in some time dependent spaces. Furthermore, we obtain analyticity of the solution.
基金Acknowledgements Fan was supported by the National Natural Science Foundation of China （Grant No. 11171154） Li was supported by the National Natural Science Foundation of China （Grant Nos. 11271184, 11671193） and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘We prove two new regularity criteria for the 3D incompressible Navier-Stokes equations in a bounded domain. Our results also hold for the 3D Boussinesq system with zero heat conductivity.
