We study the initial boundary value problem for the three-dimensional isentropic compressible Navier-Stokes equations in the exterior domain outside a rotating obstacle,with initial density having a compact support.By...We study the initial boundary value problem for the three-dimensional isentropic compressible Navier-Stokes equations in the exterior domain outside a rotating obstacle,with initial density having a compact support.By the coordinate system attached to the obstacle and an appropriate transformation of unknown functions,we obtain the three-dimensional isentropic compressible Navier-Stokes equations with a rotation effect in a fixed exterior domain.We first construct a sequence of unique local strong solutions for the related approximation problems restricted in a sequence of bounded domains,and derive some uniform bounds of higher order norms,which are independent of the size of the bounded domains.Then we prove the local existence of unique strong solution of the problem in the exterior domain,provided that the initial data satisfy a natural compatibility condition.展开更多
In this paper,we study the global existence and low Mach number limit of strong solutions to the 2-D full compressible Navier-Stokes equations around the Couette flow in a horizontally periodic layer with non-slip and...In this paper,we study the global existence and low Mach number limit of strong solutions to the 2-D full compressible Navier-Stokes equations around the Couette flow in a horizontally periodic layer with non-slip and isothermal boundary conditions.It is shown that the Couette flow is asymptotically stable for sufficiently small initial perturbations,provided that the Reynolds number,Mach number and temperature difference between the top and the lower walls are small.For the case where both the top and the lower walls maintain the same temperature,we further prove that such global strong solutions converge to a steady solution of the incompressible Navier-Stokes equations as the Mach number goes to zero.展开更多
基金supported by NSFC(11421061)by National Science Foundation of Shanghai(15ZR1403900).
文摘We study the initial boundary value problem for the three-dimensional isentropic compressible Navier-Stokes equations in the exterior domain outside a rotating obstacle,with initial density having a compact support.By the coordinate system attached to the obstacle and an appropriate transformation of unknown functions,we obtain the three-dimensional isentropic compressible Navier-Stokes equations with a rotation effect in a fixed exterior domain.We first construct a sequence of unique local strong solutions for the related approximation problems restricted in a sequence of bounded domains,and derive some uniform bounds of higher order norms,which are independent of the size of the bounded domains.Then we prove the local existence of unique strong solution of the problem in the exterior domain,provided that the initial data satisfy a natural compatibility condition.
基金supported by National Natural Science Foundation of China(Grant Nos.12131007 and 12071044)。
文摘In this paper,we study the global existence and low Mach number limit of strong solutions to the 2-D full compressible Navier-Stokes equations around the Couette flow in a horizontally periodic layer with non-slip and isothermal boundary conditions.It is shown that the Couette flow is asymptotically stable for sufficiently small initial perturbations,provided that the Reynolds number,Mach number and temperature difference between the top and the lower walls are small.For the case where both the top and the lower walls maintain the same temperature,we further prove that such global strong solutions converge to a steady solution of the incompressible Navier-Stokes equations as the Mach number goes to zero.
