由Marcus型Lévy噪声驱动的随机Hartree方程的全局适定性  

Global Well-Posedness of Stochastic Hartree Equation Driven by Lévy Noise in Marcus Form

作　　者：张朔霖 

机构地区：[1]浙江理工大学理学院,浙江 杭州

出　　处：《理论数学》2023年第10期2744-2754,共11页Pure Mathematics

摘　　要：研究随机Hartree方程在Marcus型Lévy噪声扰动下的全局适定性。选择特定条件的噪声,利用噪声规范化,得到积分方程;通过Strichartz估计和压缩映射定理研究解的局部适定性;利用伊藤公式得到解的质量守恒;应用解的一致估计研究解的全局适定性。研究结论表明:初值在Lx2空间中的随机Hartree方程在Marcus型Lévy噪声扰动下具有全局适定性和质量守恒。In this paper, Global well-posedness of Hartree equation driven by Lévy noise in Marcus form was established. Choosing special noise, taking noise in canonical form, the integral equation was give. Through Strichartz estimate and contraction mapping, local well-posedness of solution was inves-tigating, and conservation law was given by Ito formula. Finally global well-posedness was given by consistent estimate. Result of our research indicated that the Stochastic Hartree equation driven by Lévy noise has unique global solution and conservative in time when the initial value was in Lx2.

关 键 词：Hartree方程 乘性Lévy噪声 噪声规范化 It?公式 STRICHARTZ估计 质量守恒 压缩映射定理 全局适定性 

分 类 号：O17[理学—数学]