Asymptotic Stability of the Relativistic Boltzmann Equation Without Angular Cut-Off

This paper is concerned with the relativistic Boltzmann equation without angular cutoff. We establish global-in-time existence, uniqueness and asymptotic stability for solutions nearby Maxwellian. work in case of a spatially periodic box. assume generic hard-interaction soft-interaction conditions on collision kernel that were derived by Dudyński Ekiel-Je $$\dot{\text {z}}$$ ewska (Comm. Math. Phys. 115(4):607–629, 1985) [32], our assumptions include Israel particles (J. 4:1163–1181, 1963) [56]. In this physical situation, function not locally integrable, operator behaves like fractional diffusion operator. The coercivity estimates are needed rely crucially sharp asymptotics frequency multiplier has been previously established. further derive analogue Carleman dual representation resolves open question perturbative global existence Grad’s cut-off assumption.