Uniqueness for the two-dimensional Navier-Stokes equation with a measure as initial vorticity

Mathematics – Analysis of PDEs

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

32 pages

Scientific paper

We show that any solution of the two-dimensional Navier-Stokes equation whose vorticity distribution is uniformly bounded in $L^1(R^2)$ for positive times is entirely determined by the trace of the vorticity at $t = 0$, which is a finite measure. When combined with previous existence results by Cottet, by Giga, Miyakawa, and Osada, and by Kato, this uniqueness property implies that the Cauchy problem for the vorticity equation in $R^2$ is globally well-posed in the space of finite measures. In particular, this provides an example of a situation where the Navier-Stokes equation is well-posed for arbitrary data in a function space that is large enough to contain the initial data of some self-similar solutions.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Uniqueness for the two-dimensional Navier-Stokes equation with a measure as initial vorticity 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 Uniqueness for the two-dimensional Navier-Stokes equation with a measure as initial vorticity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Uniqueness for the two-dimensional Navier-Stokes equation with a measure as initial vorticity will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-347295

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.