| Abstract: |
| The Landau-Coulomb equation is a fundamental model in plasma physics that describes the statistical behavior of particles in a collisional plasma. Despite its widespread usage, the mathematical understanding of this equation has been limited due to competition between the reaction term and nonlinear, non-local diffusion term. This talk will address the global-in-time well-posedness of solutions for the homogeneous equation with Coulomb potential, when the initial data that are close to equilibrium in an $L^p$ sense. In particular, using short-time smoothing estimates, we are able to construct global-in-time classical solutions for such initial data. |
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