Tính đủ điều kiện của phương trình Schrödinger phi tuyến một chiều trong không gian điều chế
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Baoxiang, W., Lifeng, Z., Boling, G.: Isometric decomposition operators, function spaces $$E^\lambda _{p, q}$$ and applications to nonlinear evolution equations. J. Funct. Anal. 233(1), 1–39 (2006)
Bejenaru, I., Tao, T.: Sharp well-posedness and ill-posedness results for a quadratic non-linear Schrödinger equation. J. Funct. Anal. 233(1), 228–259 (2006)
Bényi, Á., Gröchenig, K., Okoudjou, K.A., Rogers, L.G.: Unimodular Fourier multipliers for modulation spaces. J. Funct. Anal. 246(2), 366–384 (2007)
Bényi, Á., Okoudjou, K.A.: Local well-posedness of nonlinear dispersive equations on modulation spaces. Bull. Lond. Math. Soc. 41(3), 549–558 (2009)
Bergh, J., Löfström, J.: Interpolation Spaces. An introduction. Grundlehren der Mathematischen Wissenschaften, No. 223. Springer, Berlin (1976)
Bhimani, D.G., Carles, R.: Norm inflation for nonlinear Schrödinger equations in Fourier-Lebesgue and modulation spaces of negative regularity. J. Fourier Anal. Appl. 26(6):Paper No.78, 34 (2020)
Bhimani, D.G., Haque, S.: Strong ill-posedness for fractional Hartree and cubic NLS equations. arXiv:2101.03991 (2021)
Bhimani, D.G., Ratnakumar, P.K.: Functions operating on modulation spaces and nonlinear dispersive equations. J. Funct. Anal. 270(2), 621–648 (2016)
Bona, J.L., Ponce, G., Saut, J.-C., Sparber, C.: Dispersive blow-up for nonlinear Schrödinger equations revisited. J. Math. Pures Appl. (9) 102(4), 782–811 (2014)
Chaichenets, L.: Modulation spaces and nonlinear Schrödinger equations. PhD thesis, Karlsruhe Institute of Technology (KIT) (2018)
Chaichenets, L., Hundertmark, D., Kunstmann, P., Pattakos, N.: On the existence of global solutions of the one-dimensional cubic NLS for initial data in the modulation space $$M_{p, q}(\mathbb{R} )$$. J. Differ. Equ. 263(8), 4429–4441 (2017)
Chaichenets, L., Hundertmark, D., Kunstmann, P., Pattakos, N.: Nonlinear Schrödinger equation, differentiation by parts and modulation spaces. J. Evol. Equ. 19(3), 803–843 (2019)
Cordero, E., Nicola, F.: Sharpness of some properties of Wiener amalgam and modulation spaces. Bull. Aust. Math. Soc. 80(1), 105–116 (2009)
Cordero, E., Okoudjou, K.A.: Dilation properties for weighted modulation spaces. J. Funct. Spaces Appl. pages Art. ID 145491, 29 (2012)
Dodson, B., Soffer, A., Spencer, T.: The nonlinear Schrödinger equation on Z and R with bounded initial data: examples and conjectures. J. Stat. Phys. 180(1–6), 910–934 (2020)
Dodson, B., Soffer, A., Spencer, T.: Global well-posedness for the cubic nonlinear Schrödinger equation with initial data lying in $$L^p$$-based Sobolev spaces. J. Math. Phys. 62(7):071507, 13 (2021)
Feichtinger, H.G.: Modulation spaces on locally compact abelian groups. In: Radha, R., Krishna, M., Thangavelu, S. (eds.) Proc. Internat. Conf. on Wavelets and Applications, pp. 1–56, Chennai, January 2002. New Delhi Allied Publishers (2003)
Gröchenig, K.: Foundations of Time-Frequency Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser Boston Inc, Boston, MA (2001)
Guo, S.: On the 1D cubic nonlinear Schrödinger equation in an almost critical space. J. Fourier Anal. Appl. 23(1), 91–124 (2017)
Killip, R., Vişan, M., Zhang, X.: Low regularity conservation laws for integrable PDE. Geom. Funct. Anal. 28(4), 1062–1090 (2018)
Klaus, F., Kunstmann, P.: Global wellposedness of NLS in $${H}^1({\mathbb{R}}) + {H}^s({\mathbb{T}})$$. J. Math. Anal. Appl. 514(2), Paper No. 126359 (2021)
Koch, H., Tataru, D.: Conserved energies for the cubic nonlinear Schrödinger equation in one dimension. Duke Math. J. 167(17), 3207–3313 (2018)
Koch, H., Tataru, D., Vişan, M.: Dispersive Equations and Nonlinear Waves. Oberwolfach Seminars, vol. 45. Birkhäuser/Springer, Basel (2014)
Molinet, L., Saut, J.C., Tzvetkov, N.: Ill-posedness issues for the Benjamin-Ono and related equations. SIAM J. Math. Anal. 33(4), 982–988 (2001)
Oh, T., Wang, Y.: Global well-posedness of the one-dimensional cubic nonlinear Schrödinger equation in almost critical spaces. J. Differ. Equ. 269(1), 612–640 (2020)
Pattakos, N.: NLS in the modulation space $$M_{2, q}({\mathbb{R} })$$. J. Fourier Anal. Appl. 25(4), 1447–1486 (2019)
Ruzhansky, M., Sugimoto, M., Wang, B.: Modulation spaces and nonlinear evolution equations. In: Evolution Equations of Hyperbolic and Schrödinger Type, volume 301 of Progr. Math., pp. 267–283. Birkhäuser/Springer Basel AG, Basel (2012)
Schippa, R.: On smoothing estimates in modulation spaces and the nonlinear Schrödinger equation with slowly decaying initial data. J. Funct. Anal. 282(5): Paper No. 109352, 46 (2022)
Schippa, R.: Infinite-energy solutions to energy-critical nonlinear Schrödinger equations in modulation spaces. J. Math. Anal. Appl. 519 (2023)
Tao, T.: Nonlinear Dispersive Equations, Local and Global Analysis, volume 106 of CBMS Regional Conference Series in Mathematics. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI (2006)
Thomas, E.G.F.: A polarization identity for multilinear maps. With an appendix by Tom H. Koornwinder. Indag. Math. (N.S.), 25(3):468–474 (2014)
Wang, B., Hudzik, H.: The global Cauchy problem for the NLS and NLKG with small rough data. J. Differ. Equ. 232(1), 36–73 (2007)