A Nash–Moser approach for the Euler–Arnold equations

被引:0
作者
Emanuel-Ciprian Cismas
Nicolae Lupa
机构
[1] Politehnica University of Timişoara,Department of Mathematics
来源
Monatshefte für Mathematik | 2020年 / 192卷
关键词
Euler equations; Nash–Moser theorem; Elliptic pseudo-differential operators; 35Q35; 35S05; 46A61; 58D05;
D O I
暂无
中图分类号
学科分类号
摘要
We study the local well-posedness in the smooth category for a class of Euler equations. A Nash–Moser approach is used to extend, for the case of an invertible elliptic pseudo-differential operator, some results obtained by Escher and Kolev, with the help of some geometric arguments.
引用
收藏
页码:333 / 353
页数:20
相关论文
共 34 条
[1]  
Arnold V(1966)Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l’hydrodynamique des fluides parfaits Ann. Inst. Fourier (Grenoble) 16 319-361
[2]  
Bauer M(2015)Local and global well-posedness of the fractional order EPDiff equation on J. Differ. Equ. 258 2010-2053
[3]  
Escher J(1993)An integrable shallow water equation with peaked solitons Phys. Rev. Lett. 71 1661-1664
[4]  
Kolev B(2014)Euler–Poincaré equations on semi-direct products Monatsh. Math. 179 491-507
[5]  
Camassa R(2016)Euler–Poincaré–Arnold equations on semi-direct products II Discrete Contin. Dyn. Syst. 36 5993-6022
[6]  
Holm DD(2000)On the blow-up rate and the blow-up set of breaking waves for a shallow water equation Math. Z. 233 75-91
[7]  
Cismas EC(2009)The hydrodynamical relevance of the Camassa–Holm and Degasperis–Procesi equations Arch. Ration. Mech. Anal. 192 165-186
[8]  
Cismas EC(2014)Right-invariant Sobolev metrics of fractional order on the diffeomorphisms group of the circle J. Geom. Mech. 6 335-372
[9]  
Constantin A(2012)Geometrical methods for equations of hydrodynamical type J. Nonlinear Math. Phys. 19 161-178
[10]  
Escher J(1982)The inverse function theorem of Nash and Moser Bull. Am. Math. Soc. 7 65-222