基于自相似解的粘性多方可压气体Navier-Stokes方程解的爆破研究

Research on Blowing up of Solution to the Viscous Polytropic Compressible Navier-Stokes Equations Based on Self-similar Solution

摘要: 通过对一维粘性多方可压缩理想气体Navier-Stokes方程解的自相似解及广义自相似解的讨论, 在具有小初值而无衰减速度的大时间行为条件下, 给出了前自相似解和后自相似解的形式, 解决了其解在整体能量估计和局部能量估计下的爆破问题。

Abstract: The paper discussed the self-similar solutions and generalized self-similar solutions to the Compressible Navier-Stokes Equations of 1D viscous polytropic ideal gas under the conditions of small initial value large time behavior without decay rate, presented out the forms of forward self-similar solutions and backward self-similar solutions, and solved the problems of blowing up of solutions under total energy and local energy estimation.