A sharp regularity result for the Euler equation with a free interface

Article type: Research Article

Authors: Kukavica, Igor^{a; *} | Tuffaha, Amjad^b

Affiliations: [a] Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA. E-mail: [email protected] | [b] Department of Mathematics and Statistics, American University of Sharjah, Sharjah, UAE. E-mail: [email protected]

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: We establish a priori estimates for local-in-time existence of solutions to the water wave model consisting of the 3D incompressible Euler equations on a domain with a free surface, without surface tension, under minimal regularity assumptions on the initial data and the Rayleigh–Taylor sign condition. The initial data are allowed to be rotational and they are assumed to belong to H2.5+δ, where δ>0 is arbitrary.

Keywords: Euler equations, free boundary, waves, local existence, Taylor condition

DOI: 10.3233/ASY-171459

Journal: Asymptotic Analysis, vol. 106, no. 2, pp. 121-145, 2018