We investigate the zero dissipation limit problem of the one-dimensional compressible isentropic Navier-Stokes equations with Riemann initial data in the case of the composite wave of two shock waves. It is shown that...We investigate the zero dissipation limit problem of the one-dimensional compressible isentropic Navier-Stokes equations with Riemann initial data in the case of the composite wave of two shock waves. It is shown that the unique solution to the Navier-Stokes equations exists for all time, and converges to the Riemann solution to the corresponding Euler equations with the same Riemann initial data uniformly on the set away from the shocks, as the viscosity vanishes. In contrast to previous related works, where either the composite wave is absent or the effects of initial layers are ignored, this gives the first mathematical justification of this limit for the compressible isentropic Navier-Stokes equations in the presence of both composite wave and initial layers. Our method of proof consists of a scaling argument, the construction of the approximate solution and delicate energy estimates.展开更多
The semiclassical limit in the transient quantum drift-diffusion equations with isentropic pressure in one space dimension is rigorously proved. The equations are supplemented with homogeneous Neumann boundary conditi...The semiclassical limit in the transient quantum drift-diffusion equations with isentropic pressure in one space dimension is rigorously proved. The equations are supplemented with homogeneous Neumann boundary conditions. It is shown that the semiclassical limit of this solution solves the classical drift-diffusion model. In the meanwhile, the global existence of weak solutions is proved.展开更多
We study the vanishing viscosity of the Navier-Stokes equations for interacting shocks. Given an entropy solution to p-system which consists of two different families of shocks interacting at some positive time,we sho...We study the vanishing viscosity of the Navier-Stokes equations for interacting shocks. Given an entropy solution to p-system which consists of two different families of shocks interacting at some positive time,we show that such entropy solution is the vanishing viscosity limit of a family of global smooth solutions to the isentropic Navier-Stokes equations. The key point of the proofs is to derive the estimates separately before and after the interaction time and connect the incoming and outgoing viscous shock profiles.展开更多
We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the isentropic compressible Navier-Stokes equations in the three space dimensions with general initial data which could...We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the isentropic compressible Navier-Stokes equations in the three space dimensions with general initial data which could be either vacuum or non-vacuum under the assumption that the viscosity coefficient μ is large enough.展开更多
The authors consider the local smooth solutions to the isentropic relativistic Euler equations in(3+1)-dimensional space-time for both non-vacuum and vacuum cases.The local existence is proved by symmetrizing the syst...The authors consider the local smooth solutions to the isentropic relativistic Euler equations in(3+1)-dimensional space-time for both non-vacuum and vacuum cases.The local existence is proved by symmetrizing the system and applying the FriedrichsLax-Kato theory of symmetric hyperbolic systems.For the non-vacuum case,according to Godunov,firstly a strictly convex entropy function is solved out,then a suitable symmetrizer to symmetrize the system is constructed.For the vacuum case,since the coefficient matrix blows-up near the vacuum,the authors use another symmetrization which is based on the generalized Riemann invariants and the normalized velocity.展开更多
We analyze the relationships between strato- spheric polar vortex anomalies and cooling events in eastern China using isentropic reanalysis data from the European Center for Medium-Range Weather Forecasts. Daily mean ...We analyze the relationships between strato- spheric polar vortex anomalies and cooling events in eastern China using isentropic reanalysis data from the European Center for Medium-Range Weather Forecasts. Daily mean data from 2000 to 2011 are used to explore the effective stratospheric signals. First, diagnoses of the 2009/2010 winter show that after the stratospheric sudden warming （SSW） of the Atlantic-East Asian （AEA） pattern, the stratospheric high isentropic potential vorticity （IPV） center derived from the split polar vortex will move to the northeast of the Eurasian continent. The air mass, accom- panied by some southward and eastward movements and characterized by high IPV values, will be stretched verti- cally, leading to apparent reinforcements of the positive vorticity and the development of acold vortex system in the troposphere. The northerly wind on the western side of the cold vortex can transport cold air southward and down- ward, resulting in this distinct cooling process in eastern China. Secondly, the empirical orthogonal function ana- lyses of IPV anomalies on the 430 K isentropic surface during 2000-2011 winters indicate that the IPV distribution and time series of the first mode are able to represent the polar vortex variation features, which significantly influ- ence cold-air activity in eastern China, especially in the AEA-type SSW winter. When the time series increases significantly, the polar vortex will be split and the high-IPV center will move to the northeast of the Eurasian continent with downward and southward developments, inducing obvious cooling in eastern China. Moreover, all the four times SSW events of AEA pattern from 2000 to 2011 are reflected in the first time series, and after the strong polar vortex disturbances, cooling processes of different inten- sities are observed in eastern China. The cooling can sus- tain at least 1 week. For this reason, the first time series can be used as an available index of polar vortex oscillation and has the power to predict 展开更多
In this paper we study the global existence and uniqueness of classical solutions to the Cauchy problem for 3D isentropic compressible Navier-Stokes equations with general initial data which could contain vacuum.We gi...In this paper we study the global existence and uniqueness of classical solutions to the Cauchy problem for 3D isentropic compressible Navier-Stokes equations with general initial data which could contain vacuum.We give the relation between the viscosity coefficients and the initial energy,which implies that the Cauchy problem under consideration has a global classical solution.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11226170,10976026 and 11271305)China Postdoctoral Science Foundation Funded Project(Grant No.2012M511640)+1 种基金Hunan Provincial Natural Science Foundation of China(Grant No.13JJ4095)National Science Foundation of USA(Grant Nos.DMS-0807406 and DMS-1108994)
文摘We investigate the zero dissipation limit problem of the one-dimensional compressible isentropic Navier-Stokes equations with Riemann initial data in the case of the composite wave of two shock waves. It is shown that the unique solution to the Navier-Stokes equations exists for all time, and converges to the Riemann solution to the corresponding Euler equations with the same Riemann initial data uniformly on the set away from the shocks, as the viscosity vanishes. In contrast to previous related works, where either the composite wave is absent or the effects of initial layers are ignored, this gives the first mathematical justification of this limit for the compressible isentropic Navier-Stokes equations in the presence of both composite wave and initial layers. Our method of proof consists of a scaling argument, the construction of the approximate solution and delicate energy estimates.
基金the National Natural Science Foundation of China(Nos.10401019,10701011,10541001)
文摘The semiclassical limit in the transient quantum drift-diffusion equations with isentropic pressure in one space dimension is rigorously proved. The equations are supplemented with homogeneous Neumann boundary conditions. It is shown that the semiclassical limit of this solution solves the classical drift-diffusion model. In the meanwhile, the global existence of weak solutions is proved.
基金supported by National Basic Research Program of China(973 Program)(Grant No.2011CB808002)the National Center for Mathematics and Interdisciplinary Sciences,Academy of Mathematics and Systems Science,Chinese Academy of Sciences and the Chinese Academy of Sciences Program for Cross&Cooperative Team of the Science&Technology Innovation,National Natural Sciences Foundation of China(Grant Nos.11171326,11371064 and 11401565)the General Research Fund of Hong Kong(Grant No.City U 103412)
文摘We study the vanishing viscosity of the Navier-Stokes equations for interacting shocks. Given an entropy solution to p-system which consists of two different families of shocks interacting at some positive time,we show that such entropy solution is the vanishing viscosity limit of a family of global smooth solutions to the isentropic Navier-Stokes equations. The key point of the proofs is to derive the estimates separately before and after the interaction time and connect the incoming and outgoing viscous shock profiles.
基金supported by National Natural Science Foundation of China (Grant No.11001090)the Fundamental Research Funds for the Central Universities (Grant No. 11QZR16)
文摘We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the isentropic compressible Navier-Stokes equations in the three space dimensions with general initial data which could be either vacuum or non-vacuum under the assumption that the viscosity coefficient μ is large enough.
基金supported by the National Natural Science Foundation of China(Nos.11201308,10971135)the Science Foundation for the Excellent Youth Scholars of Shanghai Municipal Education Commission(No.ZZyyy12025)+1 种基金the Innovation Program of Shanghai Municipal Education Commission(No.13zz136)the Science Foundation of Yin Jin Ren Cai of Shanghai Institute of Technology(No.YJ2011-03)
文摘The authors consider the local smooth solutions to the isentropic relativistic Euler equations in(3+1)-dimensional space-time for both non-vacuum and vacuum cases.The local existence is proved by symmetrizing the system and applying the FriedrichsLax-Kato theory of symmetric hyperbolic systems.For the non-vacuum case,according to Godunov,firstly a strictly convex entropy function is solved out,then a suitable symmetrizer to symmetrize the system is constructed.For the vacuum case,since the coefficient matrix blows-up near the vacuum,the authors use another symmetrization which is based on the generalized Riemann invariants and the normalized velocity.
基金supported by the National Natural Science Foundation of China(41205041)Chinese Special Fund for Meteorology(GYHY201406020)+1 种基金National Basic Research Program of China(2012CB417205)LCS Open Funds for Young Scholars(2014)
文摘We analyze the relationships between strato- spheric polar vortex anomalies and cooling events in eastern China using isentropic reanalysis data from the European Center for Medium-Range Weather Forecasts. Daily mean data from 2000 to 2011 are used to explore the effective stratospheric signals. First, diagnoses of the 2009/2010 winter show that after the stratospheric sudden warming （SSW） of the Atlantic-East Asian （AEA） pattern, the stratospheric high isentropic potential vorticity （IPV） center derived from the split polar vortex will move to the northeast of the Eurasian continent. The air mass, accom- panied by some southward and eastward movements and characterized by high IPV values, will be stretched verti- cally, leading to apparent reinforcements of the positive vorticity and the development of acold vortex system in the troposphere. The northerly wind on the western side of the cold vortex can transport cold air southward and down- ward, resulting in this distinct cooling process in eastern China. Secondly, the empirical orthogonal function ana- lyses of IPV anomalies on the 430 K isentropic surface during 2000-2011 winters indicate that the IPV distribution and time series of the first mode are able to represent the polar vortex variation features, which significantly influ- ence cold-air activity in eastern China, especially in the AEA-type SSW winter. When the time series increases significantly, the polar vortex will be split and the high-IPV center will move to the northeast of the Eurasian continent with downward and southward developments, inducing obvious cooling in eastern China. Moreover, all the four times SSW events of AEA pattern from 2000 to 2011 are reflected in the first time series, and after the strong polar vortex disturbances, cooling processes of different inten- sities are observed in eastern China. The cooling can sus- tain at least 1 week. For this reason, the first time series can be used as an available index of polar vortex oscillation and has the power to predict
基金supported by National Natural Science Foundation of China (Grant Nos.11001090 and 10971171)the Fundamental Research Funds for the Central Universities (Grant No.11QZR16)
文摘In this paper we study the global existence and uniqueness of classical solutions to the Cauchy problem for 3D isentropic compressible Navier-Stokes equations with general initial data which could contain vacuum.We give the relation between the viscosity coefficients and the initial energy,which implies that the Cauchy problem under consideration has a global classical solution.
