Global existence of bounded smooth solutions for the one-dimensional nonisetropic Euler equations

In this talk, we will introduce the global existence of bounded smooth solutions for the one-dimensional (1D) nonisentropic Euler system with large initial data. We find a sufficient condition on the initial data to obtain the global existence of bounded smooth solutions. One of the main difficulties for the global existence is that a priori C1norm estimates for the unknown functions are hard to establish. We derive a group of characteristic decompositions for the 1D full Euler equations. These characteristic decompositions can be seen as a system of  “ordinary differential equations” for the derivatives of the unknown function. Using these characteristic decompositions，we establish a priori C1 norm estimates for the solution.

报告人简介Introduction to the Speaker：

赖耕，博士毕业于上海大学数学系，曾在复旦大学数学科学学院从事博士后研究工作，现任上海大学理学院副教授。主要从事非线性双曲守恒律方程组的研究，如可压Euler方程组的二维Riemann问题、气体动力学中的激波反射问题、气体向真空扩散问题、超声速射流问题等，相关结果发表在Arch. Ration. Mech. Anal.、J. Math. Pures Appl.、SIAM J. Appl. Math.、SIAM J. Math. Anal.、Indiana Univ. Math. J.等数学期刊上。