On the Growth in time of Sobolev Norms for Time Dependent Linear Generalized KdV-type Equations
Dynamical Systems
2018-10-23 v1 Analysis of PDEs
Abstract
We give a detailed description in 1-D the growth of Sobolev norms for time dependent linear generalized KdV-type equations on the circle. For most initial data, the growth of Sobolev norms is polynomial in time for fixed analytic potential with admissible growth. If the initial data are given in a fixed smaller function space with more strict admissible growth conditions for , then the growth of previous Sobolev norms is at most logarithmic in time.
Keywords
Cite
@article{arxiv.1810.08902,
title = {On the Growth in time of Sobolev Norms for Time Dependent Linear Generalized KdV-type Equations},
author = {Chengming Cao and Xaioping Yuan},
journal= {arXiv preprint arXiv:1810.08902},
year = {2018}
}