We study the incompressible limit of classical solutions to compressible ideal magneto-hydrodynamics in a domain with a flat boundary.The boundary condition is characteristic and the initial data is general.We first e...We study the incompressible limit of classical solutions to compressible ideal magneto-hydrodynamics in a domain with a flat boundary.The boundary condition is characteristic and the initial data is general.We first establish the uniform existence of classical solutions with respect to the Mach number.Then,we prove that the solutions converge to the solution of the incompressible MHD system.In particular,we obtain a stronger convergence result by using the dispersion of acoustic waves in the half space.展开更多
电力系统运行在非理想状态时,容易产生短暂的电压波动,此时并联有源电力滤波器(shunt active power filter,SAPF)采用无源控制策略无法高效、精确地调节电能质量,而常规滑模控制又容易引起抖振。针对上述情况,将无源控制和抗干扰能力更...电力系统运行在非理想状态时,容易产生短暂的电压波动,此时并联有源电力滤波器(shunt active power filter,SAPF)采用无源控制策略无法高效、精确地调节电能质量,而常规滑模控制又容易引起抖振。针对上述情况,将无源控制和抗干扰能力更强的超螺旋二阶滑模控制相结合,提出了一种无源超螺旋二阶滑模控制策略。首先,根据有源电力滤波器的数学模型建立基于正负序分离的欧拉−拉格朗日模型;其次,对系统的模型进行了无源性分析,且根据其无源性设计了无源控制器,同时采用超螺旋二阶滑模控制对无源控制器进一步优化,提高了系统整体的鲁棒性和抗干扰能力;最后,在理想状态和负载突变、负载不平衡、电网电压不平衡、单相电压突变4种非理想状态下,通过仿真实验验证了无源超螺旋二阶滑模控制策略的有效性和优越性。展开更多
We investigate the uniform regularity and zero kinematic viscosity-magnetic diffusion limit for the incompressible viscous magnetohydrodynamic equations with the Navier boundary conditions on the velocity and perfectl...We investigate the uniform regularity and zero kinematic viscosity-magnetic diffusion limit for the incompressible viscous magnetohydrodynamic equations with the Navier boundary conditions on the velocity and perfectly conducting conditions on the magnetic field in a smooth bounded domain Ω⊂R^(3).It is shown that there exists a unique strong solution to the incompressible viscous magnetohydrodynamic equations in a finite time interval which is independent of the viscosity coefficient and the magnetic diffusivity coefficient.The solution is uniformly bounded in a conormal Sobolev space and W^(1,∞)(Ω)which allows us to take the zero kinematic viscosity-magnetic diffusion limit.Moreover,we also get the rates of convergence in L^(∞)(0,T;L^(2)),L^(∞)(0,T;W^(1,p))(2≤p<∞),and L^(∞)((0,T)×Ω)for some T>0.展开更多
文摘We study the incompressible limit of classical solutions to compressible ideal magneto-hydrodynamics in a domain with a flat boundary.The boundary condition is characteristic and the initial data is general.We first establish the uniform existence of classical solutions with respect to the Mach number.Then,we prove that the solutions converge to the solution of the incompressible MHD system.In particular,we obtain a stronger convergence result by using the dispersion of acoustic waves in the half space.
文摘电力系统运行在非理想状态时,容易产生短暂的电压波动,此时并联有源电力滤波器(shunt active power filter,SAPF)采用无源控制策略无法高效、精确地调节电能质量,而常规滑模控制又容易引起抖振。针对上述情况,将无源控制和抗干扰能力更强的超螺旋二阶滑模控制相结合,提出了一种无源超螺旋二阶滑模控制策略。首先,根据有源电力滤波器的数学模型建立基于正负序分离的欧拉−拉格朗日模型;其次,对系统的模型进行了无源性分析,且根据其无源性设计了无源控制器,同时采用超螺旋二阶滑模控制对无源控制器进一步优化,提高了系统整体的鲁棒性和抗干扰能力;最后,在理想状态和负载突变、负载不平衡、电网电压不平衡、单相电压突变4种非理想状态下,通过仿真实验验证了无源超螺旋二阶滑模控制策略的有效性和优越性。
基金supported partially by NSFC(11671193,11971234)supported partially by the China Postdoctoral Science Foundation(2019M650581).
文摘We investigate the uniform regularity and zero kinematic viscosity-magnetic diffusion limit for the incompressible viscous magnetohydrodynamic equations with the Navier boundary conditions on the velocity and perfectly conducting conditions on the magnetic field in a smooth bounded domain Ω⊂R^(3).It is shown that there exists a unique strong solution to the incompressible viscous magnetohydrodynamic equations in a finite time interval which is independent of the viscosity coefficient and the magnetic diffusivity coefficient.The solution is uniformly bounded in a conormal Sobolev space and W^(1,∞)(Ω)which allows us to take the zero kinematic viscosity-magnetic diffusion limit.Moreover,we also get the rates of convergence in L^(∞)(0,T;L^(2)),L^(∞)(0,T;W^(1,p))(2≤p<∞),and L^(∞)((0,T)×Ω)for some T>0.
