(I,J) similar solutions to Euler and NavierStokes equations
Abstract
In this paper we introduce (I,J) similar method for incompressible two and three dimensional Euler equations and NavierStokes equations, obtain a series of explicit (I,J) similar solutions to the incompressible two dimensional Euler equations, they include all of twin wave solutions, some new singularity solutions, and some global smooth solutions with finite energy. We also discover that twin wave solution and affine solution to two dimensional incompressible Euler equations are respectively plane wave and constant vector. Finally, we supply some explicit piecewise smooth solutions to incompressible three dimensional Euler and an example to incompressible three dimensional NavierStokes equations which indicates that viscosity limit of a solution to NavierStokes equations does not need to be a solution to Euler equations.
 Publication:

arXiv eprints
 Pub Date:
 July 2013
 DOI:
 10.48550/arXiv.1307.3600
 arXiv:
 arXiv:1307.3600
 Bibcode:
 2013arXiv1307.3600Y
 Keywords:

 Mathematical Physics;
 Mathematics  Analysis of PDEs