角对称区域上二维不可压理想流体方程的稳态解

Autonomous solutions of two dimension incompressible ideal fluidequations in angular symmetric domains

从分离变量出发,在圆块、圆环、锥、扇形区域、半平面等角对称区域上找到一些不可压Euler和Boussinesq方程组的显式稳态解,从中可见Euler流的流场的双曲点可任意稠密.显式解一直是偏微分方程领域中比较重要的问题,可为探讨一些理论问题提供线索.

Starting from separation of variables,explicit autonomous solutions for the 2D Euler and Boussinesq equations are obtained on angular symmetric planar domains including disks,annulus,cone,fan-shaped domains,the half-plane,etc.The hyperbolic points of Euler flows we obtained can be arbitrarily dense.Finding explicit solutions has always been important in PDE.Also,explicit solutions can provide insights in the investigations of various theoretical questions.