Title: An explicit coercivity estimate of the linearized quantum Boltzmann operator without angular cutoff Show Chinese title

Title: 无角截断下线性化量子玻尔兹曼算子的显式强制估计

Abstract: The quantum Boltzmann-Bose equation describes a large system of Bose-Einstein particles in the weak-coupling regime. If the particle interaction is governed by the inverse power law, the corresponding collision kernel has angular singularity. In this paper, we give a constructive proof of the coercivity estimate for the linearized quantum Boltzmann-Bose operator to capture the effects of the singularity and the fugacity. Precisely, the estimate explicitly reveals the dependence on the fugacity parameter before the Bose-Einstein condensation. With the coercivity estimate, the global in time well-posedness of the inhomogeneous quantum Boltzmann-Bose equation in the perturbative framework and stability of the Bose-Einstein equilibrium can be established. Show Chinese abstract

Abstract: 量子玻尔兹曼-玻色方程描述了弱耦合 regime 中的一大批玻色-爱因斯坦粒子系统。 如果粒子相互作用由反幂律控制，相应的碰撞核具有角奇异性质。 在本文中，我们给出了线性化量子玻尔兹曼-玻色算子的 coercivity 估计的构造性证明，以捕捉奇异性和逸度的影响。 精确地说，该估计明确揭示了在玻色-爱因斯坦凝聚之前对逸度参数的依赖性。 借助 coercivity 估计，可以在摄动框架中建立非均匀量子玻尔兹曼-玻色方程的全局时间适定性以及玻色-爱因斯坦平衡的稳定性。