Autonomous Solutions Of Two Dimension Incompressible Ideal Fluid Equations In Angular Symmetric Domains

Starting from separation of variables,explicit autonomous solution 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 of interest in PDE.Also,explicit solutions can provide insights in the investigations of various theoretical questions.