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Global Well-posedness of the Boltzmann Equation with Large Amplitude Initial Data  
2017-01-11 | 编辑: | 【  】【打印】【关闭

  报告题目:Global Well-posedness of the Boltzmann Equation with Large Amplitude Initial Data  

  报 告 人:王勇 中国科学院数学与系统科学研究院  

  时 间: 2017年1月14日(周六)10:00-12:00  

  地 点: 所综合楼三楼会议室  

  Abstract: The global well-posedness of the Boltzmann equation with initial data of large amplitude has remained a long-standing open problem. In this paper, by developing a new $L^\infty_xL^1_{v}\cap L^\infty_{x,v}$ approach, we prove the global existence and uniqueness of mild solutions to the Boltzmann equation in the whole space or torus for a class of initial data with bounded velocity-weighted $L^\infty$ norm under some smallness condition on $L^1_xL^\infty_v$ norm as well as defect mass, energy and entropy so that the initial data allow large amplitude oscillations. Both the hard and soft potentials with angular cut-off are considered, and the large time behavior of solutions in $L^\infty_{x,v}$ norm with explicit rates of convergence is also studied.








 
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