The formation of singularity and breakdown of classical solutions to the three- dimensional compressible viscoelasticity and inviscid elasticity are considered. For the compressible inviscid elastic fluids, the finite...The formation of singularity and breakdown of classical solutions to the three- dimensional compressible viscoelasticity and inviscid elasticity are considered. For the compressible inviscid elastic fluids, the finite-time formation of singularity in classical solu- tions is proved for certain initial data. For the compressible viscoelastic fluids, a criterion in term of the temporal integral of the velocity gradient is obtained for the breakdown of smooth solutions.展开更多
We are concerned with singularity formation of strong solutions to the two-dimensional(2D)full compressible magnetohydrodynamic equations with zero resistivity in a bounded domain.By energy method and critical Sobolev...We are concerned with singularity formation of strong solutions to the two-dimensional(2D)full compressible magnetohydrodynamic equations with zero resistivity in a bounded domain.By energy method and critical Sobolev inequalities of logarithmic type,we show that the strong solution exists globally if the temporal integral of the maximum norm of the deformation tensor is bounded.Our result is the same as Ponce’s criterion for 3D incompressible Euler equations.In particular,it is independent of the magnetic field and temperature.Additionally,the initial vacuum states are allowed.展开更多
This paper deals with the asymptotic behavior of the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with weaker decaying...This paper deals with the asymptotic behavior of the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with weaker decaying initial data, and obtains a blow-up result for C^1 solution to Cauchy problem.展开更多
The author gets a blow-up result of C1 solution to the Cauchy problem for a first order quasilinear non-strictly hyperbolic system in one space dimension.
In this paper we consider the Cauchy problem for quasilinear hyperbolic systems with characteristics with constant multiplicity. Without restriction on characteristics with constant multiplicity （〉 1）, a blow-up re...In this paper we consider the Cauchy problem for quasilinear hyperbolic systems with characteristics with constant multiplicity. Without restriction on characteristics with constant multiplicity （〉 1）, a blow-up result is obtained for the C^1 solution to the Cauchy problem under the assumptions where there is a simple genuinely nonlinear characteristic and the initial data possess certain weaker decaying properties.展开更多
For an inhomogeneous quasilinear hyperbolic system of diagonal form, under the assumptions that the system is linearly degenerate and the C^1 norm of the boundary data is bounded, we show that the mechanism of the for...For an inhomogeneous quasilinear hyperbolic system of diagonal form, under the assumptions that the system is linearly degenerate and the C^1 norm of the boundary data is bounded, we show that the mechanism of the formation of singularities of C^1 classical solution to the Goursat problem with C^1 compatibility conditions at the origin must be an ODE type. The similar result is also obtained for the weakly discontinuous solution with C^0 compatibility conditions at the origin.展开更多
基金supported in part by the National Science Foundationthe Office of Naval Research
文摘The formation of singularity and breakdown of classical solutions to the three- dimensional compressible viscoelasticity and inviscid elasticity are considered. For the compressible inviscid elastic fluids, the finite-time formation of singularity in classical solu- tions is proved for certain initial data. For the compressible viscoelastic fluids, a criterion in term of the temporal integral of the velocity gradient is obtained for the breakdown of smooth solutions.
基金partially supported by National Natural Science Foundation of China(Nos.11901474,12371227)。
文摘We are concerned with singularity formation of strong solutions to the two-dimensional(2D)full compressible magnetohydrodynamic equations with zero resistivity in a bounded domain.By energy method and critical Sobolev inequalities of logarithmic type,we show that the strong solution exists globally if the temporal integral of the maximum norm of the deformation tensor is bounded.Our result is the same as Ponce’s criterion for 3D incompressible Euler equations.In particular,it is independent of the magnetic field and temperature.Additionally,the initial vacuum states are allowed.
文摘This paper deals with the asymptotic behavior of the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with weaker decaying initial data, and obtains a blow-up result for C^1 solution to Cauchy problem.
文摘The author gets a blow-up result of C1 solution to the Cauchy problem for a first order quasilinear non-strictly hyperbolic system in one space dimension.
文摘In this paper we consider the Cauchy problem for quasilinear hyperbolic systems with characteristics with constant multiplicity. Without restriction on characteristics with constant multiplicity （〉 1）, a blow-up result is obtained for the C^1 solution to the Cauchy problem under the assumptions where there is a simple genuinely nonlinear characteristic and the initial data possess certain weaker decaying properties.
基金Supported by the National Natural Science Foundation of China(Grant No.10926162)the Fundamental Research Funds for the Central Universities(Grant No.2009B01314)the Natural Science Foundation of HohaiUniversity(Grant No.2009428011)
文摘For an inhomogeneous quasilinear hyperbolic system of diagonal form, under the assumptions that the system is linearly degenerate and the C^1 norm of the boundary data is bounded, we show that the mechanism of the formation of singularities of C^1 classical solution to the Goursat problem with C^1 compatibility conditions at the origin must be an ODE type. The similar result is also obtained for the weakly discontinuous solution with C^0 compatibility conditions at the origin.
