Regularity criteria for weak solutions to the three-dimensional MHD system
Jiao He (University of Evry - Paris Saclay)
Abstract: In this talk we will first review various known regularity criteria and partial regularity theory for 3D incompressible Navier-Stokes equations.
I will then present two generalizations of partial regularity theory of Caffarelli, Kohn and Nirenberg to the weak solutions of MHD equations. The first one is based on the framework of parabolic Morrey spaces. We will show parabolic Hölder regularity for the "suitable weak solutions" to the MHD system in small neighborhoods. This type of parabolic generalization using Morrey spaces appears to be crucial when studying the role of the pressure in the regularity theory and makes it possible to weaken the hypotheses on the pressure.
The second one is a regularity result relying on the notion of "dissipative solutions". By making use of the first result, we will show the regularity of the dissipative solutions to the MHD system with a weaker hypothesis on the pressure ($P \in \mathcal{D}'$).
This is a joint work with Diego Chamorro.
analysis of PDEsclassical analysis and ODEs
Audience: researchers in the topic
Series comments: Description: A senior graduate student/postdoc series in harmonic analysis, geometric measure theory, and partial differential equations.
Meetings will be weekly, and usually will occur on Monday, with some exceptions. For each talk, the Zoom link is made available in the website too. Contact Bruno Poggi at poggi008@umn.edu if you would like to subscribe to the seminar mailing list.
| Organizers: | Bruno Poggi*, Ryan Matzke, Jose Luis Luna Garcia* |
| *contact for this listing |