A PSEUDO-LOCAL PROPERTY OF GRAVITY WATER WAVES SYSTEM

作者：Quang Huy Nguyen^*

来源：SIAM Journal on Mathematical Analysis, 2016, 48(3): 1988-2027.

DOI：10.1137/15M1029217

• gravity water waves
• pseudo-local property
• decay property
• paradifferential calculus
• uniformly local Sobolev spaces

By proving a weighted contraction estimate in uniformly local Sobolev spaces for the flow of gravity water waves, we show that this nonlocal system is in fact pseudo-local in the following sense: locally in time, the dynamic far away from a given bounded region has a small effect on that region (again, in a sense that we will make precise in this article). Our estimate on the flow also implies a new spatial decay property of the waves. To prove this result, we establish a paradifferential calculus theory in uniformly local Sobolev spaces with weights.

• 出版日期2016