Chaos in PDEs and Lax Pairs of Euler Equations
Abstract
Description
Recently, the author and collaborators have developed a systematic program for proving the existence of homoclinic orbits in partial differential equations. Two typical forms of homoclinic orbits thus obtained are: (1). transversal homoclinic orbits, (2). Silnikov homoclinic orbits. Around the transversal homoclinic orbits in infinite dimensional autonomous systems, the author was able to prove the existence of chaos through a shadowing lemma. Around the Silnikov homoclinic orbits, the author was able to prove the existence of chaos through a horseshoe construction.
Very recently, there has been a breakthrough by the author in finding Lax pairs for Euler equations of incompressible inviscid fluids. Further results have been obtained by the author and collaborators.
Acta Appl. Math. (in press)
Acta Appl. Math. (in press)