Euler方程在Besov空间中解的存在性和解析性

发布时间：2018-04-19 01:07

本文选题：Euler方程 + 解的解析性　；参考：《青岛大学》2017年硕士论文

【摘要】：Euler方程是一种描述气体或流体运动规律的方程,它在声学,力学,水力学等领域都有着十分广泛的应用。本工作主要研究Euler方程弱解的存在性和解析性。利用先验估计和紧性方法证明了当初值u0∈B1,1s(Rn),sn+1时,弱解u ∈ C([0,T];B1,1 s(Rn))的存在唯一性,推广了 Pak和Park[22]在B1,1n+1(Rn)中Euler方程弱解的存在性的结论;Sawada O,Takada R[11]证明了在B∞,1 1中Euler方程弱解的解析性,本文研究了在空间B1,1 n|1(Rn)中Euler方程弱解的解析性。利用先验估计对非线性项的高阶导数进行处理得到合适的估计,再通过数学归纳法得到了在空间B1,11(Rn)中,当初值具有一定解析性时,方程的弱解具有相应的解析性,证明了在空间B1,1 n+1(Rn)中Euler方程弱解的解析性。
[Abstract]:The Euler equation is a description of the gas or fluid motion equations, which in acoustics, mechanics, hydraulics and other fields have a very wide range of applications. The existence of the weak solution and analysis the main research Euler equation. It is proved that using a priori estimates and compactness method when the initial value U0 = B1,1s (Rn). Sn+1, u, C ([0, T]; the weak solution of B1,1 s (Rn)) the existence and uniqueness of the extension of Pak and Park[22] in B1,1n+1 (Rn) the existence of weak solutions of Euler equation in conclusion; Sawada O, Takada R[11] proved that B - 11, analysis of the weak solution in the Euler equation in this paper, in the space B1,1 n|1 (Rn) analysis of the weak solution in the Euler equation. The high order derivative on the nonlinearity processed by appropriate estimation using a priori estimates obtained in B1,11 space by mathematical induction (Rn), the original value has certain analyticity, weak equation with the corresponding analytical solutions The analytic property of the weak solutions of the Euler equation in space B1,1 n+1 (Rn) is proved.

【学位授予单位】：青岛大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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