Stratifications planes superposées singulières et équation d'Euler 2D à temps grand Article Oct 1998 Philippe Serfati (rct 21-8-17: rg link to my other paper "Stratifications superposées singulières. analyse harmonique. commutateurs et équation d'Euler sur Rn", for its abstract2017, paper still missing)=
Abstract: We continue [19] (:Stratifications superposées singulières. analyse harmonique. commutateurs et équation d'Euler sur Rn) on short time existences in Rn, n > or = 2. We solve at large time the 2D Euler equation for data which are regular out of N intersecting regular curves and which are continuous on their non-tangential intersections. The analysis for long time existence uses some new objects, properties, techniques and tools: considering that the tangent vectors Y are more regular than the curl and gradient of the speed because the Y are continuous on all intersections, we split them and their evolution locally on two parts, one discontinuous strongly non-linear but small (because of tangential contacts or continuity on non-tangential ones which is expressed the natural compact formula (4): smallness property on tangent and non-tangent contacts) and the other continuous almost-linear. We obtain a 2x2 low-triangular almost-linear splitting system which separates their specified and incompatible treatments. The first equation is then integrable and the second one regularizes discontinuous objects into continuous ones. This last property diagonalizes the system and assures its integration and the conclusion. -- in particular we treat general 2d t-global discontinuous (superposed) vortex patches on (many) cusps and/or on corners but with VPs continuous on the points of the corners.
https://www.researchgate.net/publication/314398571_Stratifications_planes_superposees_singulieres_et_equation_d%27Euler_2D_a_temps_grand?_iepl%5BviewId%5D=kIRJPHurJSyxh3JlBcVwkOcl&_iepl%5BprofilePublicationItemVariant%5D=default&_iepl%5Bcontexts%5D%5B0%5D=prfpi&_iepl%5BinteractionType%5D=publicationTitle
Article Oct 1998 Philippe Serfati
Article Stratifications planes superposées singulières et équation d...
Article Stratifications superposées singulières. analyse harmonique. ...
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