Strichartz Estimates for Water Waves

2010/02/01 by Thomas Alazard, Nicolas Burq, Alazard, Thomas +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1002.0323

50pp

arxiv created 2010/02/01 · arxiv updated 2010/02/26

Abstract

In this paper we investigate the dispersive properties of the solutions of the two dimensional water-waves system. First we prove Strichartz type estimates with loss of derivatives at the same low level of regularity we were able to construct the solutions in [2]. On the other hand, for smoother initial data, we prove that the solutions enjoy the optimal Strichartz estimates (i.e, without loss of regularity compared to the system linearized at (? = 0, ? = 0)).

Related

• Sharp Strichartz estimates for water waves systems
• Strichartz estimates for the water-wave problem with surface tension
• Strichartz estimates and the Cauchy problem for the gravity water waves\n equations
• Strichartz estimates for the wave equation in a strictly convex domain
• Strichartz estimates for gravity water waves