完整Euler方程组的自相似解

Self-similar Solutions for Full Euler Equations

研究完整Euler方程组活塞向外均匀膨胀而产生的自相似流动问题.假设活塞以常速度各向同性地均匀膨胀,则在流动中活塞前会产生一个以恒定速度向外运动的激波阵面.在自相似假设下,该问题可简化为非线性常微分方程组带某些强加在活塞表面和激波阵面的边值条件问题.通过详细分析非线性常微分方程组的性质,证明了正光滑解的整体存在唯一性.

This paper is concerned with self-similar flows of the full Euler equations caused by the uniform expansion of piston.When the piston isotropically expands outward at a constant speed,as a result,a shock wave forms and moves outward with constant velocity.With such an assumption of self-similarity,the problem can be simplified to the nonlinear ordinary differential equations with appropriate boundary conditions imposed on the piston surface and the shock front.By analyzing the properties of nonlinear ordinary differential equations in detail,it proves the global existence and uniqueness of positive smooth solutions.