This article considers Cauchy problem for quasilinear hyperbolic systems in diagonal form. A necessary and sufficient condition in guaranteeing that Cauchy problem admits a unique global classical solution on t ≥ 0 i...This article considers Cauchy problem for quasilinear hyperbolic systems in diagonal form. A necessary and sufficient condition in guaranteeing that Cauchy problem admits a unique global classical solution on t ≥ 0 is obtained, and a sharp estimate of the life span for the classical solution is given.展开更多
The existence of global solutions, asymptotic behavior and the L^p blow-up of non-global solutions to the initial value problem are studied. We consider only the case: 1【γ【(n+2)/(n—2). It is proved that the proper...The existence of global solutions, asymptotic behavior and the L^p blow-up of non-global solutions to the initial value problem are studied. We consider only the case: 1【γ【(n+2)/(n—2). It is proved that the properties of the solutions depend only on the relations between the initial data φ(x) and the unique positive equilibrium solution. The threshold is obtained.展开更多
In this paper,we are concerned with the long time behavior of the piecewise smooth solutions to the generalized Riemann problem governed by the compressible isothermal Euler equations in two and three dimensions.A non...In this paper,we are concerned with the long time behavior of the piecewise smooth solutions to the generalized Riemann problem governed by the compressible isothermal Euler equations in two and three dimensions.A non-existence result is established for the fan-shaped wave structure solution,including two shocks and one contact discontinuity which is a perturbation of plane waves.Therefore,unlike in the one-dimensional case,the multi-dimensional plane shocks are not stable globally.Moreover,a sharp lifespan estimate is established which is the same as the lifespan estimate for the nonlinear wave equations in both two and three space dimensions.展开更多
In this article,we study the Cauchy problem to the micropolar Rayleigh–Bénard convection problem without velocity dissipation in two dimension.We first prove the local well-posedness of a smooth solution,and the...In this article,we study the Cauchy problem to the micropolar Rayleigh–Bénard convection problem without velocity dissipation in two dimension.We first prove the local well-posedness of a smooth solution,and then establish a blow up criterion in terms of the gradient of scalar temperature field.At last,we obtain the global well-posedness to the system.展开更多
基金Project supported by the NSF of China! (19971O62)the NSF of Fujian Province!(A97020) the NSF of Educational Committee of
文摘This article considers Cauchy problem for quasilinear hyperbolic systems in diagonal form. A necessary and sufficient condition in guaranteeing that Cauchy problem admits a unique global classical solution on t ≥ 0 is obtained, and a sharp estimate of the life span for the classical solution is given.
基金Project supported by the Post Doctor Foundation of China.
文摘The existence of global solutions, asymptotic behavior and the L^p blow-up of non-global solutions to the initial value problem are studied. We consider only the case: 1【γ【(n+2)/(n—2). It is proved that the properties of the solutions depend only on the relations between the initial data φ(x) and the unique positive equilibrium solution. The threshold is obtained.
基金supported by NSFC(12171097)supported in part by the Research Grants Council of the HKSAR,China(Project No.CityU 11303518,Project CityU 11304820 and Project CityU 11300021).
文摘In this paper,we are concerned with the long time behavior of the piecewise smooth solutions to the generalized Riemann problem governed by the compressible isothermal Euler equations in two and three dimensions.A non-existence result is established for the fan-shaped wave structure solution,including two shocks and one contact discontinuity which is a perturbation of plane waves.Therefore,unlike in the one-dimensional case,the multi-dimensional plane shocks are not stable globally.Moreover,a sharp lifespan estimate is established which is the same as the lifespan estimate for the nonlinear wave equations in both two and three space dimensions.
文摘In this article,we study the Cauchy problem to the micropolar Rayleigh–Bénard convection problem without velocity dissipation in two dimension.We first prove the local well-posedness of a smooth solution,and then establish a blow up criterion in terms of the gradient of scalar temperature field.At last,we obtain the global well-posedness to the system.
