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非等熵气体动力学方程组大初值问题的放缩框架

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非等熵气体动力学方程组大初值问题的放缩框架 刘树君南京财经大学应用数学学院 南京 210023 A Scaling Framework for the Non-isentropic Gas Dynamics System with Large Initial Data Shu Jun LIUSchool of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023, P. R. China
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摘要非等熵气体动力学系统Cauchy问题弱解全局存在性有两个公开问题:一个是包含真空的小初值问题,另一个是任意大初值问题.本文通过引入一个放缩框架证明了上述两个问题的等价性,即对于粘性消失解,其包含真空小初值问题的一致BV估计蕴含着任意大初值问题弱解的全局存在性.该放缩框架对大多数具有物理背景的双曲守恒律系统亦成立.
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收稿日期: 2019-08-23
MR (2010):O175.2
基金资助:国家自然科学基金资助项目(11872201);江苏省高校自然科学基金资助项目(19KJB110013)
引用本文:
刘树君. 非等熵气体动力学方程组大初值问题的放缩框架[J]. 数学学报, 2021, 64(2): 255-260. Shu Jun LIU. A Scaling Framework for the Non-isentropic Gas Dynamics System with Large Initial Data. Acta Mathematica Sinica, Chinese Series, 2021, 64(2): 255-260.
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