In this article, we are concerned with the stability of stationary solution for outflow problem on the Navier-Stokes-Poisson system. We obtain the unique existence and the asymptotic stability of stationary solution. ...In this article, we are concerned with the stability of stationary solution for outflow problem on the Navier-Stokes-Poisson system. We obtain the unique existence and the asymptotic stability of stationary solution. Moreover, the convergence rate of solution towards stationary solution is obtained. Precisely, if an initial perturbation decays with the algebraic or the exponential rate in space, the solution converges to the corresponding stationary solution as time tends to infinity with the algebraic or the exponential rate in time. The proof is based on the weighted energy method by taking into account the effect of the self-consistent electric field on the viscous compressible fluid.展开更多
This paper is concerned with an ideal polytropic model of non-viscous and heatconductive gas in a one-dimensional half space. We focus our attention on the outflow problem when the flow velocity on the boundary is neg...This paper is concerned with an ideal polytropic model of non-viscous and heatconductive gas in a one-dimensional half space. We focus our attention on the outflow problem when the flow velocity on the boundary is negative and we prove the stability of the viscous shock wave and its superposition with the boundary layer under some smallness conditions.Our waves occur in the subsonic area. The intrinsic properties of our system are more challenging in mathematical analysis, however, in the subsonic area, the lack of a boundary condition on the density provides us with a special manner for defining the shift for the viscous shock wave, and helps us to construct the asymptotic profiles successfully. New weighted energy estimates are introduced and the perturbations on the boundary are handled by some subtle estimates.展开更多
This article is devoted to studying the initial-boundary value problem for an ideal polytropic model of non-viscous and compressible gas.We focus our attention on the outflow problem when the flow velocity on the boun...This article is devoted to studying the initial-boundary value problem for an ideal polytropic model of non-viscous and compressible gas.We focus our attention on the outflow problem when the flow velocity on the boundary is negative and give a rigorous proof of the asymptotic stability of both the degenerate boundary layer and its superposition with the 3-rarefaction wave under some smallness conditions.New weighted energy estimates are introduced,and the trace of the density and velocity on the boundary are handled by some subtle analysis.The decay properties of the boundary layer and the smooth rarefaction wave also play an important role.展开更多
The outflow problem for the viscous two-phase flow model in a half line is investigated in the present paper.The existence and uniqueness of the stationary solution is shown for both supersonic state and sonic state a...The outflow problem for the viscous two-phase flow model in a half line is investigated in the present paper.The existence and uniqueness of the stationary solution is shown for both supersonic state and sonic state at spatial far field,and the nonlinear time stability of the stationary solution is also established in the weighted Sobolev space with either the exponential time decay rate for supersonic flow or the algebraic time decay rate for sonic flow.展开更多
基金supported by the National Natural Science Foundation of China(11331005,11471134)the Program for Changjiang Scholars and Innovative Research Team in University(IRT13066)the Scientific Research Funds of Huaqiao University(15BS201,15BS309)
文摘In this article, we are concerned with the stability of stationary solution for outflow problem on the Navier-Stokes-Poisson system. We obtain the unique existence and the asymptotic stability of stationary solution. Moreover, the convergence rate of solution towards stationary solution is obtained. Precisely, if an initial perturbation decays with the algebraic or the exponential rate in space, the solution converges to the corresponding stationary solution as time tends to infinity with the algebraic or the exponential rate in time. The proof is based on the weighted energy method by taking into account the effect of the self-consistent electric field on the viscous compressible fluid.
基金the Natural Science Foundation of China(11871388)。
文摘This paper is concerned with an ideal polytropic model of non-viscous and heatconductive gas in a one-dimensional half space. We focus our attention on the outflow problem when the flow velocity on the boundary is negative and we prove the stability of the viscous shock wave and its superposition with the boundary layer under some smallness conditions.Our waves occur in the subsonic area. The intrinsic properties of our system are more challenging in mathematical analysis, however, in the subsonic area, the lack of a boundary condition on the density provides us with a special manner for defining the shift for the viscous shock wave, and helps us to construct the asymptotic profiles successfully. New weighted energy estimates are introduced and the perturbations on the boundary are handled by some subtle estimates.
基金the Fundamental Research grants from the Science Foundation of Hubei Province(2018CFB693)the Natural Science Foundation of China(11871388)the Natural Science Foundation of China(11701439).
文摘This article is devoted to studying the initial-boundary value problem for an ideal polytropic model of non-viscous and compressible gas.We focus our attention on the outflow problem when the flow velocity on the boundary is negative and give a rigorous proof of the asymptotic stability of both the degenerate boundary layer and its superposition with the 3-rarefaction wave under some smallness conditions.New weighted energy estimates are introduced,and the trace of the density and velocity on the boundary are handled by some subtle analysis.The decay properties of the boundary layer and the smooth rarefaction wave also play an important role.
基金the paper is supported by the National Natural Science Foundation of China(Nos.11871047,11671384,11931010)the key research project of Academy for Multidisciplinary Studies,Capital Normal University,and by the Capacity Building for Sci-Tech Innovation-Fundamental Scientific Research Funds(No.007/20530290068).
文摘The outflow problem for the viscous two-phase flow model in a half line is investigated in the present paper.The existence and uniqueness of the stationary solution is shown for both supersonic state and sonic state at spatial far field,and the nonlinear time stability of the stationary solution is also established in the weighted Sobolev space with either the exponential time decay rate for supersonic flow or the algebraic time decay rate for sonic flow.
