| Abstract: |
| The Boltzmann equation models gas dynamics in the low density or high Mach number regime, using a statistical description of molecular interactions. Shock wave solutions have been constructed for the Boltzmann equation with hard-sphere particle interactions, and more recently for the related Landau equation of plasma dynamics by Albritton, Bedrossian, and Novack. Along similar lines as these works, we construct traveling shock solutions for the Boltzmann equation when molecular interactions are long-range. We prove existence and uniqueness up to translation near compressible Navier-Stokes shock profiles, using stability estimates for the Boltzmann equation and the stability theory of viscous shocks. |
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