Open AccessA class of large amplitude oscillating solutions for three dimensional Euler equations
Author(s) -
Christophe Cheverry,
Mekki Houbad
Publication year - 2012
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2012.11.1661
Subject(s) - euler equations , zero (linguistics) , physics , compressibility , amplitude , mathematical analysis , rank (graph theory) , domain (mathematical analysis) , semi implicit euler method , constant (computer programming) , space (punctuation) , mathematical physics , mathematics , backward euler method , combinatorics , quantum mechanics , mechanics , philosophy , linguistics , computer science , programming language
International audienceIn this article, we construct large amplitude oscillating waves, noted (uε)ε where ε∈]0,1] is a parameter going to zero, which are devised to be local solutions on some open domain of the time-space R+×R3 of both the three dimensional Burger equations (without source term), the compressible Euler equations (with some constant pressure) and the incompressible Euler equations (without pressure). The functions uε(t,x) are characterized by the fact that the corresponding Jacobian matrices Dxuε(t,x) are nilpotent of rank one or two. Our purpose is to describe the interesting geometrical features of the expressions uε(t,x) which can be obtained by this way