Scattering for a class of inhomogeneous generalized Hartree equations. (English) Zbl 1545.35185

Saanouni, Tarek; Peng, Congming

Appl. Anal. 103, No. 4, 790-806 (2024).

MSC:

35Q55

NLS equations (nonlinear Schrödinger equations)

Keywords:

inhomogeneous Hartree equation; energy; scattering; blow-up; nonlinear equations

References:

[1]	Alharbi, MG, Saanouni, T.Sharp threshold of global well-posedness vs finite time blow-up for a class of inhomogeneous Choquard equations. J Math Phys. 2019;60:081514. · Zbl 1428.35477
[2]	Alkhidhr, HA.Closed-form solutions to the perturbed NLSE with Kerr law nonlinearity in optical fibers. Results Phys. 2021;22:Article ID: 103875.
[3]	Fröhlich, J, Lenzmann, E. Mean-field limit of quantum Bose gases and nonlinear Hartree equation, Séminaire: Equations aux Dérivées Partielles 2003-2004, Sémin. Équ. Dériv. Partielles, Ecole Polytech., Palaiseau, Exp. no. XIX, 2004. p. 26. · Zbl 1292.81040
[4]	Gross, EP.Physics of many-particle systems. Vol. 1, New York: Gordon Breach; 1996.
[5]	Moroz, IM, Penrose, R, Tod, P.Spherically-symmetric solutions of the Schrödinger-Newton equations. Class Quantum Gravity. 1998;15(9):2733-2742. · Zbl 0936.83037
[6]	Abdulwahab, A. Stochastic solutions to the non-linear Schrodinger equation in optical fiber. Thermal Science. 2022; 26(1):185-190.
[7]	Lions, P-L.Some remarks on Hartree equation. Nonlinear Anal. 1981;5:1245-1256. · Zbl 0472.35074
[8]	Mohamed, EMA, Ahmed, NIA, Hussein, MIB, et al. Explanation of pressure effect for high temperature superconductors using pressure dependent Schrödinger equation and string theory. Nat Sci. 2020;12(1):28-34.
[9]	Spohn, H.On the Vlasov hierarchy. Math Method Appl Sci. 1981;3:445-455. · Zbl 0492.35067
[10]	Alghamdi, AM, Gala, S, Ragusa, MA.Global regularity for the 3D micropolar fluid flows. Filomat. 2022;36(6):1967-1970.
[11]	Boulaaras, S, Chouch, A, Ouchenane, D.General decay and well-posedness of the Cauchy problem for the Jordan-Moore-Gibson-Thompson equation with memory. Filomat. 2021;35(5):1745-1773.
[12]	Zhang, L, Yang, R, Zhang, L, et al. A conservative Crank-Nicolson Fourier spectral method for the space fractional Schrödinger equation with wave operators. J Funct Spaces. 2021;2021:Article ID 5137845. · Zbl 1498.65180
[13]	Ghanmi, R, Saanouni, T.Inhomogeneous coupled non-linear Schrödinger systems. J Math Phys. 2021;62:101508. · Zbl 1483.35223
[14]	Caoa, D, Su, Y.Minimal blow-up solutions of mass-critical inhomogeneous Hartree equation. J Math Phys. 2013;54: Article ID: 121511. · Zbl 1287.35096
[15]	Saanouni, T.Sharp threshold of global well-posedness vs finite time blow-up for a class of inhomogeneous Choquard equations. J Math Phys. 2019;60:081514. · Zbl 1428.35477
[16]	Saanouni, T, Xu, C.Scattering theory for a class of radial focusing inhomogeneous Hartree equations. Potential Anal. 2023;58:617-643. · Zbl 1512.35549
[17]	Xu, C. Scattering for the non-radial focusing inhomogeneous nonlinear Schrödinger-Choquard equation, Available at http://arxiv.org/abs/2104.09756v1.
[18]	Aksoy, NY, Sarıahmet, E.On the stability of finite difference scheme for the Schrödinger equation including momentum operator. Turk J Sci. 2022;7(2):107-115.
[19]	Iskenderov, AD, Yagubov, GY. Optimal control problem with unbounded potential for multidimensional, nonlinear and nonstationary Schrödinger equation, Proceedings of the Lankaran State University, Natural Sciences Series; 2007. p. 3-56.
[20]	Ogunniran, M, Alabi, A, Amobi, Q, et al. Fourth derivative block method for solving two-point singular boundary value problems and related stiff problems. Turk J Sci. 2021;6(2):50-60.
[21]	Ragusa, MA, Tachikawa, A.Regularity for minimizers for functionals of double phase with variable exponents. Adv Nonlinear Anal. 2020;9:710-728. · Zbl 1420.35145
[22]	Şener, SS, Celık, E, Özdemir, E.The solution of linear Volterra integral equation of the first kind with ZZ-Transform. Turk J Sci. 2021;6(3):127-133.
[23]	Toyoglu, F, Yagubov, G.Numerical solution of an optimal control problem governed by two dimensional Schrödinger equation. Appl Comput Math. 2015;4(2):30-38.
[24]	Kenig, CE, Merle, F.Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrödinger equation in the radial case. Invent Math. 2006;166(3):645-675. · Zbl 1115.35125
[25]	Tao, T.On the asymptotic behavior of large radial data for a focusing non-linear Schrödinger equation. Dyn Partial Differ Equ. 2004;1(1):1-47. · Zbl 1082.35144
[26]	Dodson, B, Murphy, J.A new proof of scattering below the ground state for the 3D radial focusing cubic NLS. Proc Amer Math Soc. 2017;145(11):4859-4867. · Zbl 1373.35287
[27]	Dinh, VD.A unified approach for energy scattering for focusing nonlinear Schrödinger equations. Discr Cont Dyn Syst. 2020;40(11):6441-6471. · Zbl 1448.35467
[28]	Moroz, V, Schaftingen, JV.Groundstates of non-linear Choquard equations: existence, qualitative properties and decay asymptotics. J Funct Anal. 2013;265:153-184. · Zbl 1285.35048
[29]	Wang, T, Yi, T.Uniqueness of positive solutions of the Choquard type equations. Appl Anal. 2017;96(3):409-417. · Zbl 1360.35256
[30]	Xiang, CL.Uniqueness and nondegeneracy of ground states for Choquard equations in three dimensions. Calc Var. 2016;55(6). · Zbl 1367.35081
[31]	Saanouni, T.Scattering versus blow-up beyond the threshold for the focusing Choquard equation. J Math Anal Appl. 2020;492(1): Article ID: 124436. · Zbl 1462.35368
[32]	Foschi, D.Inhomogeneous Strichartz estimates. J Hyperbolic Differ Equ. 2005;2(1):1-24. · Zbl 1071.35025
[33]	Keel, M, Tao, T.Endpoint Strichartz estimates. Amer J Math. 1998;120(5):955-980. · Zbl 0922.35028
[34]	Lieb, E.Analysis. 2nd ed., Providence, RI: Amer. Math. Soc.; 2001. (). · Zbl 0966.26002