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Non-viscous regularization of the Davey-Stewartson equations: Analysis and modulation theory.
- Source :
-
Journal of Mathematical Physics . 2016, Vol. 57 Issue 8, p1-22. 22p. - Publication Year :
- 2016
-
Abstract
- In the present study, we are interested in the Davey-Stewartson equations (DSE) that model packets of surface and capillary-gravity waves. We focus on the elliptic-elliptic case, for which it is known that DSE may develop a finite-time singularity. We propose three systems of non-viscous regularization to the DSE in a variety of parameter regimes under which the finite-time blow-up of solutions to the DSE occurs. We establish the global well-posedness of the regularized systems for all initial data. The regularized systems, which are inspired by the a-models of turbulence and therefore are called the a-regularized DSE, are also viewed as unbounded, singularly perturbed DSE. Therefore, we also derive reduced systems of ordinary differential equations for the α-regularized DSE by using the modulation theory to investigate the mechanism with which the proposed non-viscous regularization prevents the formation of the singularities in the regularized DSE. This is a follow-up of the work [Cao et al., Nonlinearity 21, 879-898 (2008); Cao et al., Numer. Funct. Anal. Optim. 30, 46-69 (2009)] on the non-viscous a-regularization of the nonlinear Schrödinger equation. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00222488
- Volume :
- 57
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 117902423
- Full Text :
- https://doi.org/10.1063/1.4960047