Nonlinear Dissipation for Some Systems of Critical NLS Equations in Two Dimensions
DOI:
https://doi.org/10.5890/DNC.2016.06.006Abstract
We prove the global well-posedness in H1(R2,CN) for certain systems of the critical Nonlinear Schrodinger equations coupled linearly or nonlinearly with nonlinear supercritical dissipation terms, generalizing the previous result of [1] obtained for a single equation of this kind.References
[1] Passot, T., Sulem, C., and Sulem, P.L.(2005), Linear versus nonlinear dissipation for critical NLS equation, Phys. D, 203 (3-4), 167-184.
[2] Fibich, G. and Klein, M. (2012), Nonlinear-damping continuation of the nonlinear Schrödinger equation-a numerical study, Phys. D, 241 (5), 519-527.
[3] Antonelli, P. and Sparber, C.(2010), Global well-posedness for cubic NLS with nonlinear damping, Comm. Partial Differential Equations, 35 (12), 2310-2328.
[4] Catto, I., Exner, P., and Hainzl, C.(2004), Enhanced binding revisited for a spinless particle in nonrelativistic QED, J. Math. Phys., 45(11), 4174-4185.
[5] Chen, T., Vougalter, V., and Vugalter, S. (2003), The increase of binding energy and enhanced binding in nonrelativistic QED, J. Math. Phys., 44(5), 1961-1970.
[6] Hainzl, C., Vougalter, V., and Vugalter, S. (2003), Enhanced binding in non-relativistic QED, Comm. Math. Phys., 233(1), 13-26.
[7] Pelinovsky, D.E. (2005), Inertia law for spectral stability of solitary waves in coupled nonlinear Schrödinger equations, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 461(2055), 783-812.
[8] Pelinovsky, D.E. and Yang, J.(2005), Instabilities of multihump vector solitons in coupled nonlinear Schrödinger equations, Stud. Appl. Math. 115(1), 109-137.
[9] Lieb, E. and Loss, M. (1997), Analysis, Graduate Studies in Mathematics, Volume 14 (American Mathematical Society, Providence, RI, 1997.
[10] T. Cazenave. Semilinear Schrödinger equations. Courant Lecture Notes in Mathematics, 10. New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 2003. 323 pp.
Article Metrics
Usage tracking begins September 1, 2026.