论文标题
在带有阻尼和固体芯的球形对称欧拉方程的真空无界边界问题上
On Vacuum Free Boundary Problem of the Spherically Symmetric Euler Equations with Damping and Solid Core
论文作者
论文摘要
In this paper, the global existence of smooth solution and the long-time asymptotic stability of the equilibrium to vacuum free boundary problem of the spherically symmetric Euler equations with damping and solid core have been obtained for arbitrary finite positive gas constant $A$ in the state equation $p=A ρ^γ$ with $p$ being the pressure and $ρ$ the density, provided that $γ>4/3,$ initial perturbation is small平衡$ r $的半径比实心核心$ r_0 $的半径大。此外，我们以惊人的指数时间确定速率获得了从光滑溶液到平衡的侧面收敛。该证明主要基于拉格朗日坐标中的加权能法。
In this paper, the global existence of smooth solution and the long-time asymptotic stability of the equilibrium to vacuum free boundary problem of the spherically symmetric Euler equations with damping and solid core have been obtained for arbitrary finite positive gas constant $A$ in the state equation $p=A ρ^γ$ with $p$ being the pressure and $ρ$ the density, provided that $γ>4/3,$ initial perturbation is small and the radius of the equilibrium $R$ is suitably larger than the radius of the solid core $r_0$. Moreover, we obtain the pointwise convergence from the smooth solution to the equilibrium in a surprisingly exponential time-decay rate. The proof is mainly based on weighted energy method in Lagrangian coordinate.
