This article concerns large time behavior of Ladyzhenskaya model for incompressible viscous flows in ?3. Based on linear L p -L q estimates, the auxiliary decay properties of the solutions and generalized Gronwall typ...This article concerns large time behavior of Ladyzhenskaya model for incompressible viscous flows in ?3. Based on linear L p -L q estimates, the auxiliary decay properties of the solutions and generalized Gronwall type arguments, some optimal upper and lower bounds for the decay of higher order derivatives of solutions are derived without assuming any decay properties of solutions and using Fourier splitting technology.展开更多
In this paper,we study the one-dimensional motion of viscous gas with a general pres- sure law and a general density-dependent viscosity coefficient when the initial density connects to the vacuum state with a jump.We...In this paper,we study the one-dimensional motion of viscous gas with a general pres- sure law and a general density-dependent viscosity coefficient when the initial density connects to the vacuum state with a jump.We prove the global existence and the uniqueness of weak solutions to the compressible Navier-Stokes equations by using the line method.For this,some new a priori estimates are obtained to take care of the general viscosity coefficientμ(ρ)instead ofρ~θ.展开更多
In this note,we present a framework for the large time behavior of general uniformly bounded weak entropy solutions to the Cauchy problem of Euler-Poisson system of semiconductor devices.It is shown that the solutions...In this note,we present a framework for the large time behavior of general uniformly bounded weak entropy solutions to the Cauchy problem of Euler-Poisson system of semiconductor devices.It is shown that the solutions converges to the stationary solutions exponentially in time.No smallness and regularity conditions are assumed.展开更多
基金the National Natural Science Foundation of China (Grant Nos.10241005,10771001)Natural Science Foundation of Department of Education in Anhui Province (Grant No.KJ2008A025)
文摘This article concerns large time behavior of Ladyzhenskaya model for incompressible viscous flows in ?3. Based on linear L p -L q estimates, the auxiliary decay properties of the solutions and generalized Gronwall type arguments, some optimal upper and lower bounds for the decay of higher order derivatives of solutions are derived without assuming any decay properties of solutions and using Fourier splitting technology.
基金the National Natural Science Foundation of China(Grant Nos.10625105 and 10431060)the Program for New Century Excellent Talents in University(Grant No.NCET-04-0745)
文摘In this paper,we study the one-dimensional motion of viscous gas with a general pres- sure law and a general density-dependent viscosity coefficient when the initial density connects to the vacuum state with a jump.We prove the global existence and the uniqueness of weak solutions to the compressible Navier-Stokes equations by using the line method.For this,some new a priori estimates are obtained to take care of the general viscosity coefficientμ(ρ)instead ofρ~θ.
基金the National Natural Science Foundation of China (Grant No.10471138),NSFC-NSAFG (Grant No.10676037) the Major State Basic Research Development Program of China (Grant No.2006CB805902)partially supported by NSF (Grant No.DMS-0505515)
文摘In this note,we present a framework for the large time behavior of general uniformly bounded weak entropy solutions to the Cauchy problem of Euler-Poisson system of semiconductor devices.It is shown that the solutions converges to the stationary solutions exponentially in time.No smallness and regularity conditions are assumed.
