SMOOTHING ESTIMATES FOR THE KINETIC TRANSPORT EQUATION AT THE CRITICAL REGULARITY

作者：Bez Neal^*; Cunanan Jayson; Lee Sanghyuk

来源：SIAM Journal on Mathematical Analysis, 2018, 50(2): 2280-2294.

DOI：10.1137/17M1148852

• kinetic transport equation
• averaging lemmas
• hyperbolic Sobolev spaces
• cone multiplier operator

We prove smoothing estimates for velocity averages of the kinetic transport equation in hyperbolic Sobolev spaces at the critical regularity, leading to a complete characterization 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.

• 出版日期2018