Logarithmic spikes of gradients and uniqueness of weak solutions to a class of active scalar equations

Details Logarithmic spikes of gradients and uniqueness of weak solutions to a class of active scalar equations Logarithmic spikes of gradients and uniqueness of weak solutions to a class of active scalar equations

2011-06-14

arxiv.org/abs/1106.2778v1

Mathematics

Analysis of PDEs

Scientific paper

We study the question weather weak solutions to a class of active scalar equations, with the drift velocity and the active scalar related via a Fourier multiplier of order zero, are unique. Due to some recent results we cannot expect weak solutions to be unique without additional conditions. We analyze the case of some integrability conditions on the gradient of the solutions. The condition is weaker than simply imposing $\nabla \theta \in L^\infty$. Lastly, we consider the inviscid limit for the studied class of equations.

Affiliated with

Also associated with

No associations

Rating

Logarithmic spikes of gradients and uniqueness of weak solutions to a class of active scalar equations 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 Logarithmic spikes of gradients and uniqueness of weak solutions to a class of active scalar equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Logarithmic spikes of gradients and uniqueness of weak solutions to a class of active scalar equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-114232