References
- Colin, T., Ebrard, G., Gallice, G., Texier, B. (2005). Justification of the Zakharov model from Klein-Gordon-Wave systems. Commun. Partial Differ. Equations 29(9–10):1365–1401. DOI: https://doi.org/10.1081/PDE-200037756.
- Sulem, C., Sulem, P.-L. (1999). The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse. Applied Mathematical Sciences 139. New York: Springer.
- Texier, B. (2007). Derivation of the Zakharov equations. Arch. Rational Mech. Anal. 184(1):121–183. DOI: https://doi.org/10.1007/s00205-006-0034-4.
- Zakharov, V. E. (1972). Collapse of Langmuir waves. Sov. Phys. JETP 35(5):908–914.
- Bejenaru, I., Herr, S. (2011). Convolutions of singular measures and applications to the Zakharov system. J. Funct. Anal. 261(2):478–506. DOI: https://doi.org/10.1016/j.jfa.2011.03.015.
- Bourgain, J., Colliander, J. (1996). On wellposedness of the Zakharov system. Int. Math. Res. Notices 1996(11):515–546. DOI: https://doi.org/10.1155/S1073792896000359.
- Ginibre, J., Tsutsumi, Y., Velo, G. (1997). On the Cauchy problem for the Zakharov system. J. Funct. Anal. 151(2):384–436. DOI: https://doi.org/10.1006/jfan.1997.3148.
- Bejenaru, I., Guo, Z., Herr, S., Nakanishi, K. (2015). Well-posedness and scattering for the Zakharov system in four dimensions. Anal. PDE. 8(8):2029–2055. DOI: https://doi.org/10.2140/apde.2015.8.2029.
- Bejenaru, I., Herr, S., Holmer, J., Tataru, D. (2009). On the 2D Zakharov system with L2 Schrödinger data. Nonlinearity 22(5):1063–1089. DOI: https://doi.org/10.1088/0951-7715/22/5/007.
- Candy, T., Herr, S., Nakanishi, K. (2019). The Zakharov system in dimension d≥4. J. Eur. Math. Soc. (JEMS), arXiv:1912.05820.
- Kenig, C., Ponce, G., Vega, L. (1995). On the Zakharov and Zakharov-Schulman systems. J. Funct. Anal. 127(1):204–234. DOI: https://doi.org/10.1006/jfan.1995.1009.
- Masmoudi, N., Nakanishi, K. (2008). Energy convergence for singular limits of Zakharov type systems. Invent. Math. 172(3):535–583. DOI: https://doi.org/10.1007/s00222-008-0110-5.
- Ozawa, T., Tsutsumi, Y. (1992). The nonlinear Schrödinger limit and the initial layer of the Zakharov equations. Differ. Integral Equations 5(4):721–745.
- Schochet, S. H., Weinstein, M. I. (1986). The nonlinear Schrödinger limit of the Zakharov equations governing Langmuir turbulence. Communmath. Phys. 106(4):569–580. DOI: https://doi.org/10.1007/BF01463396.
- Holmer, J., Roudenko, S. (2008). A sharp condition for scattering of the radial 3D cubic nonlinear Schrödinger equation. Commun. Math. Phys. 282(2):435–467. DOI: https://doi.org/10.1007/s00220-008-0529-y.
- Guo, Z., Nakanishi, K., Wang, S. (2013). Global dynamics below the ground state energy for the Zakharov system in the 3D radial case. Adv. Math. 238:412–441. DOI: https://doi.org/10.1016/j.aim.2013.02.008.
- Merle, F. (1996). Blow-up results of viriel type for Zakharov equations. Commun. Math. Phys. 175(2):433–455. DOI: https://doi.org/10.1007/BF02102415.
- Guo, Z., Nakanishi, K. (2014). Small energy scattering for the Zakharov system with radial symmetry. Int. Math. Res. Notes 2014(9):2327–2342. DOI: https://doi.org/10.1093/imrn/rns296.
- Guo, Z. (2016). Sharp spherically averaged Strichartz estimates for the Schrödinger equation. Nonlinearity 29(5):1668–1686. DOI: https://doi.org/10.1088/0951-7715/29/5/1668.
- Guo, Z., Lee, S., Nakanishi, K., Wang, C. (2014). Generalized Strichartz estimates and scattering for 3D Zakharov system. Commun. Math. Phys. 331(1):239–259. DOI: https://doi.org/10.1007/s00220-014-2006-0.
- Hani, Z., Pusateri, F., Shatah, J. (2013). Scattering for the Zakharov system in 3 dimensions. Commun. Math. Phys. 322(3):731–753. DOI: https://doi.org/10.1007/s00220-013-1738-6.
- Ginibre, J., Velo, G. (2006). Scattering theory for the Zakharov system. Hokkaido Math. J. 35(4):865–892. DOI: https://doi.org/10.14492/hokmj/1285766433.
- Ozawa, T., Tsutsumi, Y. (1993). Global existence and asymptotic behavior of solutions for the Zakharov equations in three space dimensions. Adv. Math. Sci. Appl. 3(94):301–334.
- Shimomura, A. (2004). Scattering theory for Zakharov equations in three-dimensional space with large data. Commun. Contemp. Math. 06(06):881–899. DOI: https://doi.org/10.1142/S0219199704001574.
- Bourgain, J. (1994). Periodic nonlinear Schrödinger equation and invariant measures. Commun. Math. Phys. 166(1):1–26. DOI: https://doi.org/10.1007/BF02099299.
- Bourgain, J. (1996). Invariant measures for the 2D-defocusing nonlinear Schrödinger equation. Commun. Math. Phys. 176(2):421–445. DOI: https://doi.org/10.1007/BF02099556.
- Burq, N., Tzvetkov, N. (2008). Random data Cauchy theory for supercritical wave equations I: local theory. Invent. Math. 173(3):449–475. DOI: https://doi.org/10.1007/s00222-008-0124-z.
- Burq, N., Tzvetkov, N. (2008). Random data Cauchy theory for supercritical wave equations II: a global existence result. Invent. Math. 173(3):477–496. DOI: https://doi.org/10.1007/s00222-008-0123-0.
- Bényi, Á., Oh, T., Pocovnicu, O. (2015). On the probabilistic Cauchy theory of the cubic nonlinear Schrödinger equation on Rd, d≥3. Trans. Amer. Math. Soc. Ser. B 2:1–50.
- Bényi, Á., Oh, T., Pocovnicu, O. (2019). Higher order expansions for the probabilistic local Cauchy theory of the cubic nonlinear Schrödinger equation on R3. Trans. Amer. Math. Soc. Ser. B 6:114–160.
- Bringmann, B. (2020). Almost sure scattering for the radial energy-critical nonlinear wave equation in three dimensions. Anal. PDE. 13(4):1011–1050. DOI: https://doi.org/10.2140/apde.2020.13.1011.
- Bringmann, B. (2018). Almost sure scattering for the energy critical nonlinear wave equation. Am. J. Math. arXiv:1812.10187.
- Dodson, B., Lührmann, J., Mendelson, D. (2019). Almost sure local well-posedness and scattering for the 4D cubic nonlinear Schrödinger equation. Adv. Math. 347:619–676. DOI: https://doi.org/10.1016/j.aim.2019.02.001.
- Dodson, B., Lührmann, J., Mendelson, D. (2020). Almost sure scattering for the 4D energy-critical defocusing nonlinear wave equation with radial data. Amer. J. Math. 142(2):475–504. DOI: https://doi.org/10.1353/ajm.2020.0013.
- Killip, R., Murphy, J., Visan, M. (2019). Almost sure scattering for the energy-critical NLS with radial data below H1(R4). Commun. Partial Differ. Equations 44(1):51–71.
- Lührmann, J., Mendelson, D. (2014). Random data Cauchy theory for nonlinear wave equations of power-type on R3. Commun. Partial Differ. Equations 39(12):2262–2283.
- Murphy, J. (2019). Random data final-state problem for the mass-subcritical NLS in L2. Proc. Amer. Math. Soc. 147(1):339–350. DOI: https://doi.org/10.1090/proc/14275.
- Nakanishi, K., Yamamoto, T. (2019). Randomized final-data problem for systems of nonlinear Schrödinger equations and the Gross-Pitaevskii equation. Math. Res. Lett. 26(1):253–279. DOI: https://doi.org/10.4310/MRL.2019.v26.n1.a12.
- Burq, N., Krieger, J. (2019). Randomization improved Strichartz estimates and global well-posedness for supercritical data. Preprint arXiv:1902.06987.
- Burq, N., Lebeau, G. (2013). Injections de Sobolev probabilistes et applications. Ann. Sci. Éc. Norm. Super. 46(6):917–962. DOI: https://doi.org/10.24033/asens.2206.
- Burq, N., Lebeau, G. (2014). Probabilistic Sobolev embeddings, applications to eigenfunctions estimates. In: Albin, P., Jakobsen, D., Rochon, F., eds. Geometric and Spectral Analysis, Vol. 630. Providence, Rhode Island: American Mathematical Society, pp. 307–318.
- Stein, E. M., Weiss, G. (1971). Introduction to Fourier Analysis on Euclidean Spaces. Princeton, NJ: Princeton University Press.
- Masmoudi, N., Nakanishi, K. (2009). Uniqueness of solutions for Zakharov systems. Funkcialaj Ekvacioj 52(2):233–253. DOI: https://doi.org/10.1619/fesi.52.233.
- Keel, M., Tao, T. (1998). Endpoint Strichartz estimates. Amer. J. Math. 120(5):955–980. DOI: https://doi.org/10.1353/ajm.1998.0039.
- Christ, M., Kiselev, A. (2001). Maximal functions associated to filtrations. J. Funct. Anal. 179(2):409–425. DOI: https://doi.org/10.1006/jfan.2000.3687.
- Tao, T. (1999). Spherically averaged endpoint Strichartz estimates for the two-dimensional Schrödinger equation. Commun. Partial Differ. Equations 25(7–8):1471–1485. DOI: https://doi.org/10.1080/03605300008821556.
- Tzvetkov, N. (2010). Construction of a Gibbs measure associated to the periodic Benjamin-Ono equation. Probab. Theory Relat. Fields 146(3–4):481–514. DOI: https://doi.org/10.1007/s00440-008-0197-z.
- Bényi, Á., Oh, T., Pocovnicu, O. (2015). Wiener randomization on unbounded domains and an application to almost sure well-posedness of NLS. In: Balan, R., et al., eds. Excursions in Harmonic Analysis, Vol. 4. Cham: Birkhäuser, pp. 3–25.
- Sterbenz, J. (2005). Angular regularity and Strichartz estimates for the wave equation, with an appendix by I. Int. Math. Res. Notices 2005(4):187–231. DOI: https://doi.org/10.1155/IMRN.2005.187.
- Bergh, J., Löfström, J. (1976). Interpolation spaces. An introduction. In: Chern, S. S., et al., eds. Grundlehren der Mathematischen Wissenschaften, Vol. 223. Berlin: Springer-Verlag.