메뉴 건너뛰기




Volumn 44, Issue 5, 2011, Pages 855-903

Strichartz estimates for water waves

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84856758959     PISSN: 00129593     EISSN: None     Source Type: Journal    
DOI: 10.24033/asens.2156     Document Type: Article
Times cited : (36)

References (31)
  • 2
    • 79959880152 scopus 로고    scopus 로고
    • On the water-wave equations with surface tension
    • T. ALAZARD, N. BURQ, C. ZUILY, On the water-wave equations with surface tension, Duke Math. J. 158(2011), 413-499.
    • (2011) Duke Math. J. , vol.158 , pp. 413-499
    • Alazard, T.1    Burq, N.2    Zuily, C.3
  • 3
    • 74949116792 scopus 로고    scopus 로고
    • Paralinearization of the Dirichlet to Neumann operator, and regularity of three-dimensional water waves
    • T. ALAZARD, G. METIVIER, Paralinearization of the Dirichlet to Neumann operator, and regularity of three-dimensional water waves, Comm. Partial Differential Equations 34(2009), 1632-1704.
    • (2009) Comm. Partial Differential Equations , vol.34 , pp. 1632-1704
    • Alazard, T.1    Metivier, G.2
  • 4
    • 0040695843 scopus 로고
    • Paracomposition et opérateurs paradifférentiels
    • S. ALINHAC, Paracomposition et opérateurs paradiffé rentiels, Comm. Partial Differential Equations 11(1986), 87-121.
    • (1986) Comm. Partial Differential Equations , vol.11 , pp. 87-121
    • Alinhac, S.1
  • 5
    • 0000310274 scopus 로고
    • Existence d'ondes de raréfaction pour des systèmes quasi-linéaires hyperboliquesmultidimensionnels
    • S. ALINHAC, Existence d'ondes de raréfaction pour des systèmes quasi-linéaires hyperboliquesmultidimensionnels, Comm. Partial Differential Equations 14(1989), 173-230.
    • (1989) Comm. Partial Differential Equations , vol.14 , pp. 173-230
    • Alinhac, S.1
  • 6
    • 26944460000 scopus 로고    scopus 로고
    • The zero surface tension limit of two-dimensional water waves
    • DOI 10.1002/cpa.20085
    • D. M. AMBROSE, N. MASMOUDI, The zero surface tension limit of two-dimensional water waves, Comm. Pure Appl. Math. 58(2005), 1287-1315. (Pubitemid 41482566)
    • (2005) Communications on Pure and Applied Mathematics , vol.58 , Issue.10 , pp. 1287-1315
    • Ambrose, D.M.1    Masmoudi, N.2
  • 7
    • 0033474442 scopus 로고    scopus 로고
    • Équations d'ondes quasilinéaires et estimations de Strichartz
    • H. BAHOURI, J.-Y. CHEMIN, Équations d'ondes quasilinéaires et estimations de Strichartz, Amer J. Math. 121(1999), 1337-1377.
    • (1999) Amer J. Math. , vol.121 , pp. 1337-1377
    • Bahouri, H.1    Chemin, J.-Y.2
  • 9
    • 0003360898 scopus 로고
    • Interpolation spaces. An introduction
    • Springer
    • J. BERGH, J. LÖFSTRÖM, Interpolation spaces. An introduction, Grundl. Math. Wiss. 223, Springer, 1976.
    • (1976) Grundl. Math. Wiss. , vol.223
    • Bergh, J.1    Löfström, J.2
  • 10
    • 0032136390 scopus 로고    scopus 로고
    • On the cauchy problem for a capillary drop. Part I: Irrotational motion
    • K. BEYER, M. GUNTHER, On the Cauchy problem for a capillary drop. I. Irrotational motion, Math. Methods Appl. Sci. 21(1998), 1149-1183. (Pubitemid 128590493)
    • (1998) Mathematical Methods in the Applied Sciences , vol.21 , Issue.12 , pp. 1149-1183
    • Beyer, K.1    Gunther, M.2
  • 11
    • 33646370539 scopus 로고    scopus 로고
    • Strichartz estimates for wave equations with coefficients of sobolev regularity
    • DOI 10.1080/03605300600635053, PII U7665016722711
    • M. BLAIR, Strichartz estimates for wave equations with coefficients of Sobolev regularity, Comm. Partial Differential Equations 31(2006), 649-688. (Pubitemid 43663649)
    • (2006) Communications in Partial Differential Equations , vol.31 , Issue.5 , pp. 649-688
    • Blair, M.1
  • 12
    • 0001191104 scopus 로고
    • Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires
    • J.-M. BONY, Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires, Ann. Sci. École Norm. Sup. 14(1981), 209-246.
    • (1981) Ann. Sci. École Norm. Sup. , vol.14 , pp. 209-246
    • Bony, J.-M.1
  • 13
    • 2942564358 scopus 로고    scopus 로고
    • Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds
    • N. BURQ, P. GERARD, N. TZVETKOV, Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds, Amer J. Math. 126(2004), 569-605. (Pubitemid 38749562)
    • (2004) American Journal of Mathematics , vol.126 , Issue.3 , pp. 569-605
    • Burq, N.1    Gerard, P.2    Tzvetkov, N.3
  • 14
    • 36749078690 scopus 로고    scopus 로고
    • On well-posedness for the Benjamin-Ono equation
    • N. BURQ, F. PLANCHON, On well-posedness for the Benjamin-Ono equation, Math. Ann. 340(2008), 497-542.
    • (2008) Math. Ann. , vol.340 , pp. 497-542
    • Burq, N.1    Planchon, F.2
  • 15
    • 0003312241 scopus 로고
    • Fluides parfaits incompressibles
    • J.-Y. CHEMIN, Fluides parfaits incompressibles, Astérisque 230 (1995).
    • (1995) Astérisque , pp. 230
    • Chemin, J.-Y.1
  • 17
    • 34548446988 scopus 로고    scopus 로고
    • Well-posedness of the free-surface incompressible Euler equations with or without surface tension
    • D. COUTAND, S. SHKOLLER, Well-posedness of the free-surface incompressible Euler equations with or without surface tension, J. Amer. Math. Soc. 20(2007), 829-930.
    • (2007) J. Amer. Math. Soc. , vol.20 , pp. 829-930
    • Coutand, D.1    Shkoller, S.2
  • 18
    • 67650725448 scopus 로고    scopus 로고
    • Global solutions for the gravity water waves equation in dimension 3
    • P. GERMAIN, N. MASMOUDI, J. SHATAH, Global solutions for the gravity water waves equation in dimension 3, C R. Math. Acad. Sci. Paris 347(2009), 897-902.
    • (2009) C R. Math. Acad. Sci. Paris , vol.347 , pp. 897-902
    • Germain, P.1    Masmoudi, N.2    Shatah, J.3
  • 19
    • 33847163682 scopus 로고    scopus 로고
    • A long wave approximation for capillary-gravity waves and an effect of the bottom
    • T. IGUCHI, A long wave approximation for capillary-gravity waves and an effect of the bottom, Comm. Partial Differential Equations 32(2007), 37-85.
    • (2007) Comm. Partial Differential Equations , vol.32 , pp. 37-85
    • Iguchi, T.1
  • 20
    • 11844267209 scopus 로고    scopus 로고
    • Dispersive estimates for principally normal pseudodifferential operators
    • H. KOCH, D. TATARU, Dispersive estimates for principally normal pseudodifferential operators, Comm. Pure Appl. Math. 58(2005), 217-284.
    • (2005) Comm. Pure Appl. Math. , vol.58 , pp. 217-284
    • Koch, H.1    Tataru, D.2
  • 21
    • 77958104591 scopus 로고    scopus 로고
    • Para-differential calculus and applications to the Cauchy problem for nonlinear systems
    • EdizionidellaNormale, Pisa
    • G. METIVIER, Para-differential calculus and applications to the Cauchy problem for nonlinear systems, Centro di Ricerca Matematica Ennio De Giorgi (CRM) Series 5, EdizionidellaNormale, Pisa, 2008.
    • (2008) Centro di Ricerca Matematica Ennio de Giorgi (CRM) Series , vol.5
    • Metivier, G.1
  • 22
    • 71549133352 scopus 로고    scopus 로고
    • Well-posedness of the water-wave problem with surface tension
    • M. MING, Z. ZHANG, Well-posedness of the water-wave problem with surface tension, J. Math. PuresAppl. 92(2009), 429-455.
    • (2009) J. Math. PuresAppl. , vol.92 , pp. 429-455
    • Ming, M.1    Zhang, Z.2
  • 23
    • 77953866714 scopus 로고    scopus 로고
    • On the transverse instability of one dimensional capillarygravity waves
    • F. ROUSSET, N. TZVETKOV, On the transverse instability of one dimensional capillarygravity waves, Discrete Contin. Dyn. Syst. Ser B 13(2010), 859-872.
    • (2010) Discrete Contin. Dyn. Syst. Ser B , vol.13 , pp. 859-872
    • Rousset, F.1    Tzvetkov, N.2
  • 25
    • 52349104032 scopus 로고    scopus 로고
    • Geometry and a priori estimates for free boundary problems of the Euler equation
    • J. SHATAH, C. ZENG, Geometry and a priori estimates for free boundary problems of the Euler equation, Comm. Pure Appl. Math. 61(2008), 698-744.
    • (2008) Comm. Pure Appl. Math. , vol.61 , pp. 698-744
    • Shatah, J.1    Zeng, C.2
  • 27
    • 0036383355 scopus 로고    scopus 로고
    • Strichartz estimates for a Schrödinger operator with nonsmooth coefficients
    • G. STAFFILANI, D. TATARU, Strichartz estimates for a Schrödinger operator with nonsmooth coefficients, Comm. Partial Differential Equations 27(2002), 1337-1372.
    • (2002) Comm. Partial Differential Equations , vol.27 , pp. 1337-1372
    • Staffilani, G.1    Tataru, D.2
  • 28
    • 0034164787 scopus 로고    scopus 로고
    • Strichartz estimates for operators with nonsmooth coefficients and the nonlinear wave equation
    • D. TATARU, Strichartz estimates for operators with nonsmooth coefficients and the nonlinear wave equation, Amer. J. Math. 122(2000), 349-376.
    • (2000) Amer. J. Math. , vol.122 , pp. 349-376
    • Tataru, D.1
  • 29
    • 0035373942 scopus 로고    scopus 로고
    • Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients, II
    • D. TATARU, Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients. II, Amer. J. Math. 123(2001), 385-423. (Pubitemid 33405619)
    • (2001) American Journal of Mathematics , vol.123 , Issue.3 , pp. 385-423
    • Tataru, D.1
  • 30
    • 67650433790 scopus 로고    scopus 로고
    • Almost global wellposedness of the 2-D full water wave problem
    • S. WU, Almost global wellposedness of the 2-D full water wave problem, Invent. Math. 177(2009), 45-135.
    • (2009) Invent. Math. , vol.177 , pp. 45-135
    • Wu, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.