On the Strichartz estimates for the kinetic transport equation
Jonathan Bennett, Neal Bez, Susana Gutierrez, Sanghyuk Lee
TL;DR
This paper demonstrates that the endpoint Strichartz estimate for the kinetic transport equation does not hold in any dimension and introduces a new multilinear analysis approach for non-endpoint cases.
Contribution
It proves the non-validity of the endpoint estimate and offers a novel multilinear method for establishing non-endpoint Strichartz estimates.
Findings
Endpoint estimate is false in all dimensions.
New multilinear approach for non-endpoint estimates.
Provides a deeper understanding of kinetic transport equations.
Abstract
We show that the endpoint Strichartz estimate for the kinetic transport equation is false in all dimensions. We also present a new approach to proving the non-endpoint cases using multilinear analysis.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Numerical methods in inverse problems · Lattice Boltzmann Simulation Studies