Local well-posedness for the periodic Boltzmann equation with constant collision kernel

2024/11/19 by Başakoğlu, Engin, Tzvetkov, Nikolay, Sun, Chenmin +1 · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2411.12140

Abstract

We study the Boltzmann equation with the constant collision kernel in the case of spatially periodic domain \mathbbT^d, d≥ 2. Using the existing techniques from nonlinear dispersive PDEs, we prove the local well-posedness result in L^2,r_vH^s_x for s>(d)/(2)-(1)/(4) and r>(d)/(2). To reach the result, the main tool we establish is the L⁴ Strichartz estimate for solutions to the corresponding linear equation.

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• Sharp L⁴ Strichartz estimate for Hyperbolic Schrödinger equation on ℝ× \mathbbT

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