STABILITY OF THE NONRELATIVISTIC VLASOV-MAXWELL-BOLTZMANN SYSTEM FOR ANGULAR NON-CUTOFF POTENTIALS RENJUN DUAN, SHUANGQIAN LIU, TONG YANG, AND HUIJIANG ZHAO Abstract. Although there recently have been extensive studies on the pertur- bation theory of the angular non-cutoff Boltzmann equation (cf. [4] and [17]), it remains mathematically unknown when there is a self-consistent Lorentz force coupled with the Maxwell equations in the nonrelativistic approxima- tion. In the paper, for perturbative initial data with suitable regularity and integrability, we establish the large time stability of solutions to the Cauchy problem on the Vlasov-Maxwell-Boltzmann system with physical angular non- cutoff intermolecular collisions including the inverse power law potentials, and also obtain as a byproduct the convergence rates of solutions. The proof is based on a refined time-velocity weighted energy method with two key tech- nical parts: one is to introduce the exponentially weighted estimates into the non-cutoff Boltzmann operator and the other to design a delicate temporal en- ergy X(t)-norm to obtain its uniform bound. The result also extends the case of the hard sphere model considered by Guo (Invent. Math. 153(3): 593–630 (2003)) to the general collision potentials. Contents 1. Introduction 2 1.1. The Cauchy problem 2 1.2. Reformulation, weight and norm 4 1.3. Main result 6 2. Weighted estimates on Γ and L 9 2.1. Weighted estimates on Γ 9 2.2. Weighted estimates on L 22 3. Global a priori estimates 24 3.1. Macro structure and macro dissipation 25 3.2. Uniform spatial energy estimate 26 3.3. The highest-order energy estimate with weight 29 3.4. Decay of electromagnetic fields and macro components 36 3.5. The compensating energy estimate with weight 39 3.6. Decay of the lower order energy 40 3.7. Global existence 43 Appendix A. 44 References 45 Date : July 18, 2013.