-
86浏览
-
0点赞
-
0收藏
-
0分享
-
0下载
-
0评论
-
引用
期刊论文
Almost Global Existence for 2-D Incompressible Isotropic Elastodynamics
arXiv,-0001,(): | arXiv:1212.6391
We consider the Cauchy problem for 2-D incompressible isotropic elastodynamics. Standard energy methods yield local solutions on a time interval [0,T/ϵ], for initial data of the form ϵU0, where T depends only on some Sobolev norm of U0. We show that for such data there exists a unique solution on a time interval [0,expT/ϵ], provided that ϵ is sufficiently small. This is achieved by careful consideration of the structure of the nonlinearity. The incompressible elasticity equation is inherently linearly degenerate in the isotropic case; in other words, the equation satisfies a null condition. This is essential for time decay estimates. The pressure, which arises as a Lagrange multiplier to enforce the incompressibility constraint, is estimated in a novel way as a nonlocal nonlinear term with null structure. The proof employs the generalized energy method of Klainerman, enhanced by weighted L2 estimates and the ghost weight introduced by Alinhac.
【免责声明】以下全部内容由[雷震]上传于[2021年03月24日 10时56分28秒],版权归原创者所有。本文仅代表作者本人观点,与本网站无关。本网站对文中陈述、观点判断保持中立,不对所包含内容的准确性、可靠性或完整性提供任何明示或暗示的保证。请读者仅作参考,并请自行承担全部责任。
本学者其他成果
同领域成果