Long-time Existence for Systems of Quasilinear Wave Equations
Long-time Existence for Systems of Quasilinear Wave Equations
复制标题
拟线性波动方程组的长期存在性
DOI：
10.1007/s44007-022-00036-9
复制
发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Rhoads, Taylor
中科院分区：
文献类型：
--
作者：
Metcalfe, Jason;Rhoads, Taylor
We consider quasilinear wave equations in (1 + 3)-dimensions where the nonlinearity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F(u, u^{\prime } , u^{\prime \prime })$$\end{document} is permitted to depend on the solution rather than just its derivatives. For scalar equations, if, almost global existence was established by Lindblad. We seek to show a related almost global existence result for coupled systems of such equations. To do so, we will rely upon a variant of the-weighted local energy estimate of Dafermos and Rodnianski that includes a ghost weight akin to those used by Alinhac. The decay that is needed to close the argument comes from space–time Klainerman–Sobolev type estimates from the work of Metcalfe, Tataru, and Tohaneanu.
We consider quasilinear wave equations in (1 + 3)-dimensions where the nonlinearity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F(u, u^{\prime } , u^{\prime \prime })$$\end{document} is permitted to depend on the solution rather than just its derivatives. For scalar equations, if, almost global existence was established by Lindblad. We seek to show a related almost global existence result for coupled systems of such equations. To do so, we will rely upon a variant of the-weighted local energy estimate of Dafermos and Rodnianski that includes a ghost weight akin to those used by Alinhac. The decay that is needed to close the argument comes from space–time Klainerman–Sobolev type estimates from the work of Metcalfe, Tataru, and Tohaneanu.
影响因子：
1.7
作者：
D. Tataru
通讯作者：
D. Tataru
时间相关非捕获背景上标量场的局部能量衰减
影响因子：
1.7
作者：
Jason Metcalfe;Jacob Sterbenz;D. Tataru
通讯作者：
D. Tataru