Incompressible limit for the 2D isentropic Euler system with critical initial data

Details Incompressible limit for the 2D isentropic Euler system with critical initial data Incompressible limit for the 2D isentropic Euler system with critical initial data

2012-03-17

arxiv.org/abs/1203.3871v1

Mathematics

Analysis of PDEs

22 pages

Scientific paper

We study in this paper the low Mach number limit for the 2d isentropic Euler system with ill-prepared initial data belonging to the critical Besov space $B_{2,1}^2$. By combining Strichartz estimates with the special structure of the vorticity we prove that the lifespan goes to infinity as the Mach number goes to zero. We also prove the strong convergence in the space of the initial data $B_{2,1}^2$ of the incompressible parts to the solution of the incompressible Euler system. There are at least two main difficulties: the first one concerns the Beale-Kato-Majda criterion which is not known to work for rough regularities. However, the second one is related to the critical aspect of the quantity $\Vert(\textnormal{div}\,v_{\varepsilon},\nabla c_{\varepsilon})\Vert_{L_{T}^{1}L^\infty}$ which has the scale of $B_{2,1}^2$ in the space variable.

Affiliated with

Also associated with

No associations

Rating

Incompressible limit for the 2D isentropic Euler system with critical initial data does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Incompressible limit for the 2D isentropic Euler system with critical initial data, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Incompressible limit for the 2D isentropic Euler system with critical initial data will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-313136