半线性广义Tricomi方程Cauchy问题解的生命跨度估计研究

半线性广义Tricomi方程是来自气体动力学中的模型，最近，其小初值Cauchy问题解的大时间行为受到越来越多的关注。国内外数学工作者感兴趣的是该问题什么时候存在整体解，什么时候解会在有限时间内破裂。已有的工作表明其存在一个临界指标，该临界指标与空间维数、非线性项指数及Tricomi算子有关系。本项目计划研究半线性广义Tricomi方程小初值Cauchy问题解在有限时间内破裂时解的生命跨度估计，进一步加深对气体动力学物理现象的理解。

The semilinear generalized Tricomi equation naturally arises in the physical problems of gas dynamics, the small data Cauchy problem of which attracts more and more attention recently. For this problem, people are interested in determining when it has global solution and when the solution will blow up in a finite time. The known results imply that the problem admits a critical exponent, which depends on the space dimensions, the power of the nonlinear term and the Tricomi operator. This project aims to study the lifespan estimate of the Cauchy problem for the semilinear generalized Tricomi equation with small data, which will be helpful to understand the physical phenomenon of gas dynamics.