arXiv subjects

Yachun Li

Publications and source records attributed to Yachun Li.

39 records · Page 3Linked to original sources

arXiv2014

On regular solutions of the 3-D compressible isentropic Euler-Boltzmann equations with vacuum

In this paper, we discuss the Cauchy Problem for the compressible isentropic Euler-Boltzmann equations with vacuum in radiation hydrodynamics. Firstly, we establish the local existence of regular solutions by the fundamental methods in the theory of quasi-linear symmetric hyperbolic systems under some physical assumptions. Then we give the non-global existence of regular solutions caused by the effect of vacuum for $1<γ\leq 3$. Finally, we extend our result to the initial-boundary value problem under some suitable boundary conditions. These blow-up results tell us that the radiation cannot prevent the formation of singularities caused by the appearance of vacuum.

math-ph↗

arXiv2014

On Neumann boundary problem for strongly degenerate parabolic-hyperbolic equations on a bounded rectangle

We study a Neumann type initial-boundary value problem for strongly degenerate parabolic-hyperbolic equations under the nonlinearity-diffusivity condition. We suggest a notion of entropy solution for this problem and prove its uniqueness. The existence of entropy solutions is also discussed.

math.AP↗

arXiv2014

Formation of singularities in solutions to the compressible radiation hydrodynamics equations with vacuum

We study the Cauchy problem for multi-dimensional compressible radiation hydrodynamics equations with vacuum. First, we present some sufficient conditions on the blow-up of smooth solutions in multi-dimensional space. Then, we obtain the invariance of the support of density for the smooth solutions with compactly supported initial mass density by the property of the system under the vacuum state. Based on the above-mentioned results, we prove that we cannot get a global classical solution, no matter how small the initial data are, as long as the initial mass density is of compact support. Finally, we will see that some of the results that we obtained are still valid for the isentropic flows with degenerate viscosity coefficients as well as 1-D case.

math-ph↗