In this paper,we consider the 3D magnetic Bénard problem.More precisely,we prove that the large solutions are stable under certain conditions.And we obtain the equivalent condition with respect to this stability ...In this paper,we consider the 3D magnetic Bénard problem.More precisely,we prove that the large solutions are stable under certain conditions.And we obtain the equivalent condition with respect to this stability condition.Finally,we also establish the stability of 2 D magnetic Bénard problem under 3D perturbations.展开更多
In this article,we study the Cauchy problem to the micropolar Rayleigh–Bénard convection problem without velocity dissipation in two dimension.We first prove the local well-posedness of a smooth solution,and the...In this article,we study the Cauchy problem to the micropolar Rayleigh–Bénard convection problem without velocity dissipation in two dimension.We first prove the local well-posedness of a smooth solution,and then establish a blow up criterion in terms of the gradient of scalar temperature field.At last,we obtain the global well-posedness to the system.展开更多
We investigate the thermal instability of a three-dimensional Rayleigh–Bénard(RB for short)problem without thermal diffusion in a bounded domain.First we construct unstable solutions in exponential growth modes ...We investigate the thermal instability of a three-dimensional Rayleigh–Bénard(RB for short)problem without thermal diffusion in a bounded domain.First we construct unstable solutions in exponential growth modes for the linear RB problem.Then we derive energy estimates for the nonlinear solutions by a method of a prior energy estimates,and establish a Gronwall-type energy inequality for the nonlinear solutions.Finally,we estimate for the error of L^(1)-norm between the both solutions of the linear and nonlinear problems,and prove the existence of escape times of nonlinear solutions.Thus we get the instability of nonlinear solutions under L^(1)-norm.展开更多
基金supported partially by NSFC(11571380,11971497,11871230)Natural Science Foundation of GuangDong Province(2019B151502041)+3 种基金supported partially by NSFC(11126266)Natural Science Foundation of GuangDong Province(2016A030313390)SCAU Fund for High-level University Buildingsupported partially by NSFC(11971496)。
文摘In this paper,we consider the 3D magnetic Bénard problem.More precisely,we prove that the large solutions are stable under certain conditions.And we obtain the equivalent condition with respect to this stability condition.Finally,we also establish the stability of 2 D magnetic Bénard problem under 3D perturbations.
文摘In this article,we study the Cauchy problem to the micropolar Rayleigh–Bénard convection problem without velocity dissipation in two dimension.We first prove the local well-posedness of a smooth solution,and then establish a blow up criterion in terms of the gradient of scalar temperature field.At last,we obtain the global well-posedness to the system.
基金supported by the NSF of China(Grant No.11901100)the Natural Science Foundation of Fujian Province of China(Grant No.2020J02001)Funds of Education Department of Fujian Province(Grant No.510881/GXRC-20046)。
文摘We investigate the thermal instability of a three-dimensional Rayleigh–Bénard(RB for short)problem without thermal diffusion in a bounded domain.First we construct unstable solutions in exponential growth modes for the linear RB problem.Then we derive energy estimates for the nonlinear solutions by a method of a prior energy estimates,and establish a Gronwall-type energy inequality for the nonlinear solutions.Finally,we estimate for the error of L^(1)-norm between the both solutions of the linear and nonlinear problems,and prove the existence of escape times of nonlinear solutions.Thus we get the instability of nonlinear solutions under L^(1)-norm.
