带阻尼项的欧拉方程初边值问题的经典解

Classical solution of initial-boundary value problem for Euler equations with damping

研究一维空间中带非线性阻尼项的等熵欧拉方程Dirichlet初边值问题经典解的整体存在唯一性.在其初边值问题局部解存在的条件下,利用能量估计的方法,得到当初值在平衡解附近小扰动时,非线性阻尼项对方程组解的存在性没有影响,其经典解仍整体存在唯一.

The global existence and uniqueness of the classical solution for Dirichlet initial-boundary value problem for one-dimensional isentropie Euler equations with nonlinear damping is studied. On Condition that the local solution for the initial-boundary value problem is existed, it is obtained that with perturbation of the initial value, the nonlinear damping does not influence the existence of the solution, the classical solution is still existed and unique, by using energy estimates.