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arXiv · 1709.04146

Smoothing estimates for the kinetic transport equation at the critical regularity

Neal Bez·Jayson Cunanan·Sanghyuk Lee
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Abstract

We prove smoothing estimates for velocity averages of the kinetic transport equation in hyperbolic Sobolev spaces at the critical regularity, leading to a complete characterisation of the allowable regularity exponents. Such estimates will be deduced from some mixed-norm estimates for the cone multiplier operator at a certain critical index. Our argument is not particular to the geometry of the cone and we illustrate this by establishing analogous estimates for the paraboloid.

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Neal Bez, Jayson Cunanan, Sanghyuk Lee. 2017-09-13. Smoothing estimates for the kinetic transport equation at the critical regularity. https://doi.org/10.1137/17m1148852

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