The water-wave equations: From Zakharov to Euler

Progress in Nonlinear Differential Equations and Their Application

Volumn 84, Issue , 2013, Pages 1-20

  Alazard, Thomas ^a   Burq, Nicolas ^b   Zuily, Claude ^b  

^a CNRS   (France)

^b Université Paris Sud 11   (France)

Author keywords

Cauchy theory; Euler equations; Water wave system

Indexed keywords

EID: 85034844876     PISSN: 14211750     EISSN: 23740280     Source Type: Book Series    
DOI: 10.1007/978-1-4614-6348-1_1     Document Type: Chapter

References (7)

1. Alazard, T., Burq, N., Zuily, C.: On the water-wave equations with surface tension. Duke Math. J. 158(3), 413–499 (2011)
2. Alazard, T., Burq, N., Zuily, C.: On the Cauchy problem for gravity water waves. Preprint (2012) arxiv:1212.0626
3. Craig, W., Sulem, C.: Numerical simulation of gravity waves. J. Comput. Phys. 108(1), 73–83 (1993)
4. Lannes, D.: Well-posedness of the water-waves equations. J. Am. Math. Soc. 18(3), 605–654 (electronic) (2005)
5. Lannes, D.: Water waves: mathematical analysis and asymptotics. to appear
6. Wu, S.: Well-posedness in Sobolev spaces of the full water wave problem in 2-D. Invent. Math. 130(1), 39–72 (1997)
7. Zakharov, V.E.: Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 9(2), 190–194 (1968)