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Chaos in PDEs and Lax Pairs of Euler Equations

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Abstract

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.

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  1. Department of Mathematics, University of Missouri, Columbia, MO, 65211, U.S.A.

    Yanguang (Charles) Li

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Li, Y.(. Chaos in PDEs and Lax Pairs of Euler Equations. Acta Applicandae Mathematicae 77, 181–214 (2003). https://doi.org/10.1023/A:1024024001070

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