Global well-posedness for the incompressible viscoelastic fluids in the critical $L^p$ framework

Details Global well-posedness for the incompressible viscoelastic fluids in the critical $L^p$ framework Global well-posedness for the incompressible viscoelastic fluids in the critical $L^p$ framework

2011-01-31

arxiv.org/abs/1101.5864v2

Mathematics

Analysis of PDEs

20 pages

Scientific paper

We investigate global strong solutions for the incompressible viscoelastic system of Oldroyd--B type with the initial data close to a stable equilibrium. We obtain the existence and uniqueness of the global solution in a functional setting invariant by the scaling of the associated equations, where the initial velocity has the same critical regularity index as for the incompressible Navier--Stokes equations, and one more derivative is needed for the deformation tensor. Like the classical incompressible Navier-Stokes, one may construct the unique global solution for a class of large highly oscillating initial velocity. Our result also implies that the deformation tensor $F$ has the same regularity as the density of the compressible Navier--Stokes equations.

Affiliated with

Also associated with

No associations

Rating

Global well-posedness for the incompressible viscoelastic fluids in the critical $L^p$ framework 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 Global well-posedness for the incompressible viscoelastic fluids in the critical $L^p$ framework, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Global well-posedness for the incompressible viscoelastic fluids in the critical $L^p$ framework will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-647110