The global Cauchy problem for a local alignment model with a relaxational inter-particle interaction operator is considered. More precisely, we consider the global-in-time existence of weak solutions of BGK model with local velocity-alignment term when the initial data have finite mass, momentum, energy, and entropy. The analysis involves weak/strong compactness based on the velocity moments estimates and several velocity-weighted $ L^\infty $ estimates.

中文翻译：

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具有局部速度对准力的BGK动力学模型

考虑具有松弛粒子间相互作用算子的局部对准模型的整体柯西问题。更确切地说，当初始数据具有有限的质量，动量，能量和熵时，我们考虑具有局部速度对齐项的BGK模型的弱解的全局时间存在性。该分析涉及基于速度矩估计值和几个速度加权$ L ^ \ infty $估计值的弱/强紧实度。