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Volumn 159, Issue 1, 2005, Pages 187-223

Bilinear eigenfunction estimates and the nonlinear Schrödinger equation on surfaces

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EID: 12144282712     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00222-004-0388-x     Document Type: Article
Times cited : (152)

References (39)
  • 3
    • 0030158684 scopus 로고    scopus 로고
    • On the ill posedness of the IVP for the generalized KdV and NLS equations
    • Birnir, B., Kenig, C.E., Ponce, G., Svanstedt, N., Vega, L.: On the ill posedness of the IVP for the generalized KdV and NLS equations. J. Lond. Math. Soc. 53, 551-559 (1996)
    • (1996) J. Lond. Math. Soc. , vol.53 , pp. 551-559
    • Birnir, B.1    Kenig, C.E.2    Ponce, G.3    Svanstedt, N.4    Vega, L.5
  • 4
    • 34250084341 scopus 로고
    • Fourier transform restriction phenomena for certain lattice subsets and application to nonlinear evolution equations i. Schrödinger equations
    • Bourgain, J.: Fourier transform restriction phenomena for certain lattice subsets and application to nonlinear evolution equations i. Schrödinger equations. Geom. Funct. Anal. 3, 107-156 (1993)
    • (1993) Geom. Funct. Anal. , vol.3 , pp. 107-156
    • Bourgain, J.1
  • 5
    • 0000710855 scopus 로고
    • Exponential sums and nonlinear Schrödinger equations
    • Bourgain, J.: Exponential sums and nonlinear Schrödinger equations. Geom. Funct. Anal. 3, 157-178 (1993)
    • (1993) Geom. Funct. Anal. , vol.3 , pp. 157-178
    • Bourgain, J.1
  • 9
    • 46449111550 scopus 로고    scopus 로고
    • The Cauchy problem for the nonlinear Schrödinger equation on a compact manifold
    • Proceedings of the Öresund Symposium on Partial Differential Equations, Lund, May 2002
    • Burq, N., Gérard, P., Tzvetkov, N.: The Cauchy problem for the nonlinear Schrödinger equation on a compact manifold. Proceedings of the Öresund Symposium on Partial Differential Equations, Lund, May 2002. J. Nonlinear Math. Phys. 10, 1-16 (2003)
    • (2003) J. Nonlinear Math. Phys. , vol.10 , pp. 1-16
    • Burq, N.1    Gérard, P.2    Tzvetkov, N.3
  • 10
    • 2942564358 scopus 로고    scopus 로고
    • Strichartz inequalities and the non linear Schrödinger equation on compact manifolds
    • Burq, N., Gérard, P., Tzvetkov, N.: Strichartz inequalities and the non linear Schrödinger equation on compact manifolds. Am. J. Math. 126, 569-605 (2004)
    • (2004) Am. J. Math. , vol.126 , pp. 569-605
    • Burq, N.1    Gérard, P.2    Tzvetkov, N.3
  • 12
    • 0000692012 scopus 로고
    • Oscillatory integrals and a multiplier problem for the disc
    • Carleson, L., Sjölin, P.: Oscillatory integrals and a multiplier problem for the disc. Stud. Math. 44, 287-299 (1972)
    • (1972) Stud. Math. , vol.44 , pp. 287-299
    • Carleson, L.1    Sjölin, P.2
  • 14
    • 0348218177 scopus 로고    scopus 로고
    • Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations
    • Christ, M., Colliander, J., Tao, T.: Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations. Am. J. Math. 125, 1235-1293 (2003)
    • (2003) Am. J. Math. , vol.125 , pp. 1235-1293
    • Christ, M.1    Colliander, J.2    Tao, T.3
  • 16
    • 51249186551 scopus 로고
    • Le spectre des opérateurs elliptiques à bicaractéristiques toutes periodiques
    • Colin de Verdière, Y.: Le spectre des opérateurs elliptiques à bicaractéristiques toutes periodiques. Comment. Math. Helv. 54, 508-522 (1979)
    • (1979) Comment. Math. Helv. , vol.54 , pp. 508-522
    • Colin De Verdière, Y.1
  • 17
    • 0042229265 scopus 로고    scopus 로고
    • Bilinear space-time estimates for homogeneous wave equations
    • Foschi, D., Klainerman, S.: Bilinear space-time estimates for homogeneous wave equations. Ann. Sci. Éc. Norm. Supér. 33, 211-274 (2000)
    • (2000) Ann. Sci. Éc. Norm. Supér. , vol.33 , pp. 211-274
    • Foschi, D.1    Klainerman, S.2
  • 18
    • 0035217268 scopus 로고    scopus 로고
    • Profile decomposition for the wave equation outside a convex obstacle
    • Gallagher, I., Gérard, P.: Profile decomposition for the wave equation outside a convex obstacle. J. Math. Pures Appl., IX. Sér. 80, 1-49 (2001)
    • (2001) J. Math. Pures Appl., IX. Sér. , vol.80 , pp. 1-49
    • Gallagher, I.1    Gérard, P.2
  • 20
    • 33747492074 scopus 로고    scopus 로고
    • Le problème de Cauchy pour des edp semi-linéaires périodiques en variables d'espace (d'après Bourgain)
    • Ginibre, J.: Le problème de Cauchy pour des edp semi-linéaires périodiques en variables d'espace (d'après Bourgain). Séminaire Bourbaki 1995, Astérisque 237, 163-187 (1996)
    • (1996) Séminaire Bourbaki 1995, Astérisque , vol.237 , pp. 163-187
    • Ginibre, J.1
  • 21
    • 84972548521 scopus 로고
    • Lectures on spectral theory of elliptic operators
    • Guillemin, V.: Lectures on spectral theory of elliptic operators. Duke Math. J. 44, 129-137 (1977)
    • (1977) Duke Math. J. , vol.44 , pp. 129-137
    • Guillemin, V.1
  • 23
    • 0002820858 scopus 로고
    • Fourier integral operators. I
    • Hörmander, L.: Fourier integral operators. I. Acta Math. 127, 79-183 (1971)
    • (1971) Acta Math. , vol.127 , pp. 79-183
    • Hörmander, L.1
  • 26
    • 0001442617 scopus 로고    scopus 로고
    • On the ill-posedness of some canonical dispersive equations
    • Kenig, C.E., Ponce, G., Vega, L.: On the ill-posedness of some canonical dispersive equations. Duke Math. J. 106, 617-633 (2001)
    • (2001) Duke Math. J. , vol.106 , pp. 617-633
    • Kenig, C.E.1    Ponce, G.2    Vega, L.3
  • 27
    • 1842535994 scopus 로고    scopus 로고
    • Remark on Strichartz-type inequalities. With appendices by J. Bourgain and D. Tataru
    • Klainerman, S., Machedon, M.: Remark on Strichartz-type inequalities. With appendices by J. Bourgain and D. Tataru. Int. Math. Res. Not. 5, 201-220 (1996)
    • (1996) Int. Math. Res. Not. , vol.5 , pp. 201-220
    • Klainerman, S.1    Machedon, M.2
  • 30
    • 0035738686 scopus 로고    scopus 로고
    • Non linear optic and supercritical wave equation
    • Hommage à Pascal Laubin
    • Lebeau, G.: Non linear optic and supercritical wave equation. Bull. Soc. R. Sci. Liège 70, 267-306 (2002), Hommage à Pascal Laubin
    • (2002) Bull. Soc. R. Sci. Liège , vol.70 , pp. 267-306
    • Lebeau, G.1
  • 31
    • 0039479479 scopus 로고
    • Trüdinger type inequalities and uniqueness of weak solutions for the nonlinear Schrödinger equation
    • Ogawa, T., Ozawa, T.: Trüdinger type inequalities and uniqueness of weak solutions for the nonlinear Schrödinger equation. J. Math. Anal. Appl. 155, 531-540 (1991)
    • (1991) J. Math. Anal. Appl. , vol.155 , pp. 531-540
    • Ogawa, T.1    Ozawa, T.2
  • 32
    • 0003140505 scopus 로고
    • Oscillatory integrals and spherical harmonics
    • Sogge, C.: Oscillatory integrals and spherical harmonics. Duke Math. J. 53, 43-65 (1986)
    • (1986) Duke Math. J. , vol.53 , pp. 43-65
    • Sogge, C.1
  • 33
    • 0001371314 scopus 로고
    • P norm of spectral clusters for second order elliptic operators on compact manifolds
    • P norm of spectral clusters for second order elliptic operators on compact manifolds. J. Funct. Anal. 77, 123-138 (1988)
    • (1988) J. Funct. Anal. , vol.77 , pp. 123-138
    • Sogge, C.1
  • 35
    • 0036383355 scopus 로고    scopus 로고
    • Strichartz estimates for a Schrödinger operator with nonsmooth coefficients
    • Staffilani, G., Tataru, D.: Strichartz estimates for a Schrödinger operator with nonsmooth coefficients. Commun. Partial Differ. Equations 27, 1337-1372 (2002)
    • (2002) Commun. Partial Differ. Equations , vol.27 , pp. 1337-1372
    • Staffilani, G.1    Tataru, D.2
  • 37
    • 0035486554 scopus 로고    scopus 로고
    • 2 functions, and applications to nonlinear dispersive equations
    • 2 functions, and applications to nonlinear dispersive equations. Am. J. Math. 123, 839-908 (2001)
    • (2001) Am. J. Math. , vol.123 , pp. 839-908
    • Tao, T.1
  • 38
    • 0038564013 scopus 로고
    • On the solvability of mixed problem for a nonlinear equation of Schrödinger type
    • Vladimirov, M.V.: On the solvability of mixed problem for a nonlinear equation of Schrödinger type. Sov. Math. Dokl. 29, 281-284 (1984)
    • (1984) Sov. Math. Dokl. , vol.29 , pp. 281-284
    • Vladimirov, M.V.1
  • 39
    • 12144285199 scopus 로고
    • Nonlinear stabilization of quasimodes
    • Proc. A.M.S. Symp. on Geometry of the Laplacian, Hawaii, 1979
    • Weinstein, A.: Nonlinear stabilization of quasimodes. Proc. A.M.S. Symp. on Geometry of the Laplacian, Hawaii, 1979, A.M.S. Colloq. Publ. 36, 301-318 (1980)
    • (1980) A.M.S. Colloq. Publ. , vol.36 , pp. 301-318
    • Weinstein, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.