Global Stability of the Boltzmann Equation for a Polyatomic Gas with Initial Data Allowing Large Oscillations

2024/07/18 by Ko, Gyounghun, Son, Sung-jun · 1 citation
#35Q20 #76P05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2407.13192

Abstract

In this paper, we consider the Boltzmann equation for a polyatomic gas. We establish that the mild solution to the Boltzmann equation on the torus is globally well-posed, provided the initial data that satisfy bounded velocity-weighted L^∞ norm and the smallness condition on the initial relative entropy. Furthermore, we also study the asymptotic behavior of solutions, converging to the global Maxwellian with an exponential rate. A key point in the proof is to develop the pointwise estimate on the gain term of non-linear collision operator for Grönwall's argument.

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• Regularity Theory for the Space Homogeneous Polyatomic Boltzmann Flow

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