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In this paper, we study the singular vortex patches in the two-dimensional incompressible Navier-Stokes equations. We show, in particular, that if the initial vortex patch is C1+s outside a singular set Σ, so the velocity is, for all time, lipschitzian outside the image of Σ through the viscous flow. In addition, the correponding lipschitzian norm is independent of the viscosity. This allows us to prove some results related to the inviscid limit for the geometric structures of the vortex patch.
Hmidi, Taoufik. "Poches de tourbillon singulières dans un fluide faiblement visqueux.." Revista Matemática Iberoamericana 22.2 (2006): 489-543. <http://eudml.org/doc/41982>.
@article{Hmidi2006, author = {Hmidi, Taoufik}, journal = {Revista Matemática Iberoamericana}, keywords = {Ecuaciones de Navier-Stokes; Ecuación de Euler; Fluidos incompresibles; Vorticidad; Singularidades; Navier-Stokes equations; Euler equations; vortex patches; Littlewood-Paley theory}, language = {fre}, number = {2}, pages = {489-543}, title = {Poches de tourbillon singulières dans un fluide faiblement visqueux.}, url = {http://eudml.org/doc/41982}, volume = {22}, year = {2006}, }
TY - JOUR AU - Hmidi, Taoufik TI - Poches de tourbillon singulières dans un fluide faiblement visqueux. JO - Revista Matemática Iberoamericana PY - 2006 VL - 22 IS - 2 SP - 489 EP - 543 LA - fre KW - Ecuaciones de Navier-Stokes; Ecuación de Euler; Fluidos incompresibles; Vorticidad; Singularidades; Navier-Stokes equations; Euler equations; vortex patches; Littlewood-Paley theory UR - http://eudml.org/doc/41982 ER -