带非线性阻尼项的等熵欧拉方程组的整体解

带非线性阻尼项的等熵欧拉方程组的整体解 The Global Solutions of the Isentropic Euler Equations with Nonlinear Damping 朱旭生 ZHU Xusheng1 1 first-author 熊显萍 XIONG Xianping2 2 涂爱花 TU Aihua1 1 华东交通大学基础科学学院 华东交通大学基础科学学院 School of Basic Science,East China Jiaotong University School of Basic Science,East China Jiaotong University 兴义民族师范学院数学系 兴义民族师范学院数学系 Department of Mathematics,Xingyi Normal University for Nationalities,Xingyi Department of Mathematics,Xingyi Normal University for Nationalities,Xingyi 研究带非线性阻尼项的一维等熵欧拉方程组的Cauchy问题,阻尼系数有正的下界.当初始数据是常状态附近的小扰动时,利用能量估计法,证明了经典解的整体存在.利用傅立叶分析法得到整体经典解在大时间时的衰减性. The Cauchy problem for the 1-D isentropic Euler equations with nonlinear damping is investigated in this paper,while the damping efficient has a positive bound below.The global classic solution is obtained provided the initial data is a perturbation of a constant state by utilizing energy estimates.Moreover,the decays rates of the global solution are obtained by using Fourier transform method. 等熵欧拉方程组 非线性阻尼 能量估计 傅立叶变换 衰减估计 the isentropic Euler equations nonlinear damping energy estimates Fourier transform decay estimates 10.14188/j.1671-8836.2011.02.008 O175.27 江西省自然科学基金资助项目（2007GZS0811） 2011-02-01 2021-04-01 2 57