On global attractors for 2D damped driven nonlinear Schrödinger equations

References

• Nozaki K, Bekki N. Low-dimensional chaos in a driven damped nonlinear Schrödinger equation. Phys D. 1986;21:381–393.
   Google Scholar
• Blow KJ, Doran NJ. Global and local chaos in the pumped nonlinear Schrödinger equation. Phys Rev Lett. 1984;52:526–529.
   Web of Science ®Google Scholar
• Haken H. Laser theory. Berlin: Springer; 1984.
   Google Scholar
• Nussenzveig H. Introduction to quantum optics. London: Gordon and Breach; 1973.
   Google Scholar
• Cazenave T. Semilinear Schrödinger equations. New York: AMS; 2003.
   Google Scholar
• Ghidaglia JM. Finite-dimensional behaviour for weakly damped driven Schrödinger equations. Ann Inst Henri Poincaré. 1988;5:365–405.
   Web of Science ®Google Scholar
• Abounouh M. Asymptotic behavior for a weakly damped Schrödinger equation in dimension two. Appl Math Lett. 1993;6:29–32.
   Web of Science ®Google Scholar
• Abounouh M, Goubet O. Attractor for a damped cubic Schrödinger equation on a two-dimensional thin domain. Differ Integral Equ. 2000;13(1–3):311–340.
   Google Scholar
• Laurençot P. Long-time behaviour for weakly damped driven nonlinear Schrödinger equations in RN, N≤3. Nonlinear Differ Equ Appl. 1995;2(3):357–369.
   Google Scholar
• Ghidaglia JM, Heron B. Dimension of the attractors associated to the Ginzburg–Landau partial differential equation. Physica D. 1987;28:282–304.
   Google Scholar
• Ball J. Global attractors for damped semilinear wave equations. Discrete Cont Dyn Syst. 2004;10(1/2):31–52.
   Web of Science ®Google Scholar
• Goubet O. Regularity of the attractor for the weakly damped nonlinear Schrödinger equation. Appl Anal. 1996;60:99–119.
   Google Scholar
• Goubet O. Regularity of the attractor for a weakly damped nonlinear Schrödinger equation in R2. Adv Differ Equ. 1998;3:337–360.
   Google Scholar
• Goubet O, Molinet L. Global attractor for weakly damped nonlinear Schrödinger equations in L2(R). Nonlinear Anal Theory Methods Appl. 2009;71:317–320. hal-00421278.
   Google Scholar
• Tao T. A global compact attractor for high-dimensional defocusing non-linear Schrödinger equations with potential. Dyn PDE. 2008;5:101–116.
   Google Scholar
• Saanouni T. Nonlinear damped Schrödinger equation in two space dimensions. Electron J Differ Equ. 2015;2015(121):1–9.
   Google Scholar
• Cazenave T, Han Z. Asymptotic behavior for a Schrödinger equation with nonlinear subcritical dissipation. Discrete Cont Dyn Syst A. 2020;40(8):4801–4819.
   Web of Science ®Google Scholar
• Haraux A. Two remarks on dissipative hyperbolic problems. In: Brezis H, Lions JL, editors. Nonlinear partial differential equations and their applications. College de France Seminar. Vol. VII. Research Notes in Mathematics. Vol. 122. London: Pitman; 1985. p. 161–179.
   Google Scholar
• Haraux A. Systèmes dynamiques dissipatifs et applications, R.M.A. 17. Collection dirigée par Ph. Ciarlet et Lions JL. Paris: Masson; 1991.
   Google Scholar
• Wang X. An energy equation for the weakly damped driven nonlinear Schrödinger equations and its application to their attractors. Phys D. 1995;88:167–175.
   Google Scholar
• Moise I, Rosa R, Wang X. Attractors for noncompact nonautonomous systems via energy equations. Discrete Cont Dyn Syst. 2004;10(1):473–496.
   Web of Science ®Google Scholar
• Chepyzhov VV, Vishik MI. Attractors for equations of mathematical physics. Providence (RI): AMS; 2002.
   Google Scholar
• Zelik SV. Strong uniform attractors for non-autonomous dissipative PDEs with non translation-compact external forces. Discrete Cont Dyn Syst Ser B. 2015;20(3):781–810.
   Web of Science ®Google Scholar
• Hale J. Ordinary differential equations. Malabar (FL): Krieger; 1980.
   Google Scholar
• Adams RA. Sobolev spaces. New York: Academic; 1975.
   Google Scholar
• Chepyzhov VV, Vishik MI. Non-autonomous dynamical systems and their attractors. In: Vishik M, editor. Asymptotic behaviour of solutions of evolutionary equations. Cambridge: Cambridge University Press; 1992. p. 111–150.
   Google Scholar
• Chepyzhov VV, Vishik MI. A Hausdorff dimension estimate for kernel sections of non-autonomous evolution equations. Indiana Univ Math J. 1993;42(2):1057–1076.
   Google Scholar
• Lions J-L. Quelques méthodes de résolution des problèmes aux limites non linéaires. Gauthier-Villars, Paris: Dunod; 1969.
   Google Scholar