On the behaviors of solution near possible blow-up time in the incompressible Euler and related equations

Details On the behaviors of solution near possible blow-up time in the incompressible Euler and related equations On the behaviors of solution near possible blow-up time in the incompressible Euler and related equations

2008-07-24

arxiv.org/abs/0807.3927v1

Mathematics

Analysis of PDEs

25 pages

Scientific paper

We study behaviors of scalar quantities near the possible blow-up time, which is made of smooth solutions of the Euler equations, Navier-Stokes equations and the surface quasi-geostrophic equations. Integrating the dynamical equations of the scaling invariant norms, we derive the possible blow-up behaviors of the above quantities, from which we obtain new type of blow-up criteria and some necessary conditions for the blow-up.

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