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# Local well-posedness for the Boltzmann equation with very soft potential and polynomially decaying initial data

### Analysis, Dynamics, and Applications Seminar

Local well-posedness for the Boltzmann equation with very soft potential and polynomially decaying initial data
Series: Analysis, Dynamics, and Applications Seminar
Location: Hybrid: Math 402/Online
Presenter: Weinan Wang, Department of Mathematics, University of Arizona

We consider the local well-posedness of the spatially inhomogeneous non-cutoff Boltzmann equation when the initial data decays polynomially in the velocity variable. We consider the case of very soft potentials $\gamma + 2s < 0$. Our main result completes the picture for local well-posedness in this decay class by removing the restriction $\gamma + 2s > -3/2$ of previous works. It is based on the Carleman decomposition of the collision operator into a lower order term and an integro-differential operator similar to the fractional Laplacian.

Hybrid: Math 402 and