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Volumn 33, Issue 10, 2008, Pages 1862-1889

Cubic nonlinear schrödinger equation on three dimensional balls with radial data

Author keywords

Bilinear Strichartz estimate; Nonlinear Schr dinger equation; X s,b spaces; Zeroes of Bessel functions

Indexed keywords


EID: 54049119716     PISSN: 03605302     EISSN: 15324133     Source Type: Journal    
DOI: 10.1080/03605300802402591     Document Type: Article
Times cited : (18)

References (29)
  • 1
    • 0000710855 scopus 로고
    • Exponential sums and nonlinear Schrödinger equations
    • Bourgain, J. (1993). Exponential sums and nonlinear Schrödinger equations. Geom. Funct. Anal. 3:157-178.
    • (1993) Geom. Funct. Anal , vol.3 , pp. 157-178
    • Bourgain, J.1
  • 2
    • 34250084341 scopus 로고
    • Fourier transform restriction phenomena for certain lattice subsets and application to nonlinear evolution equations i. Schrödinger equations
    • Bourgain, J. (1993). Fourier transform restriction phenomena for certain lattice subsets and application to nonlinear evolution equations i. Schrödinger equations. Geom. Funct. Anal. 3:107-156.
    • (1993) Geom. Funct. Anal , vol.3 , pp. 107-156
    • Bourgain, J.1
  • 3
    • 0003230767 scopus 로고    scopus 로고
    • Global Solutions of Nonlinear Schrödinger Equations
    • Providence, RI: American Mathematical Society
    • Bourgain, J. (1999). Global Solutions of Nonlinear Schrödinger Equations. American Mathematical Society Colloquium Publications, 46. Providence, RI: American Mathematical Society.
    • (1999) American Mathematical Society Colloquium Publications, 46
    • Bourgain, J.1
  • 4
    • 49149142420 scopus 로고
    • Nonlinear Schrödinger evolution equations
    • Brézis, H., Gallouet, T. (1980). Nonlinear Schrödinger evolution equations. Nonlin. Anal. TMA 4:677-681.
    • (1980) Nonlin. Anal. TMA , vol.4 , pp. 677-681
    • Brézis, H.1    Gallouet, T.2
  • 5
    • 84855856274 scopus 로고    scopus 로고
    • An example of singular dynamics for the nonlinear Schrödinger equation on bounded domains
    • Colombini, F, Nishitani, T, eds. Hyperbolic Problems and Related Topics, Somerville, MA: International Press, pp
    • Burq, N., Gérard, P., Tzvetkov, N. (2003). An example of singular dynamics for the nonlinear Schrödinger equation on bounded domains. In: Colombini, F., Nishitani, T., eds. Hyperbolic Problems and Related Topics. Graduated series in Analysis. Somerville, MA: International Press, pp. 57-66.
    • (2003) Graduated series in Analysis , pp. 57-66
    • Burq, N.1    Gérard, P.2    Tzvetkov, N.3
  • 6
    • 0038238334 scopus 로고    scopus 로고
    • Two singular dynamics of the nonlinear Schrödinger equation on a plane domain
    • Burq, N., Gérard, P., Tzvetkov, N. (2003). Two singular dynamics of the nonlinear Schrödinger equation on a plane domain. Geom. Funct. Anal. 13:1-19.
    • (2003) Geom. Funct. Anal , vol.13 , pp. 1-19
    • Burq, N.1    Gérard, P.2    Tzvetkov, N.3
  • 7
    • 2942564358 scopus 로고    scopus 로고
    • Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds
    • Burq, N., Gérard, P., Tzvetkov, N. (2004). Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds. Amer. J. Math. 126:569-605.
    • (2004) Amer. J. Math , vol.126 , pp. 569-605
    • Burq, N.1    Gérard, P.2    Tzvetkov, N.3
  • 8
    • 12144282712 scopus 로고    scopus 로고
    • Bilinear eigenfunction estimates and the nonlinear Schrödinger equation on surfaces
    • Burq, N., Gérard, P., Tzvetkov, T. (2005). Bilinear eigenfunction estimates and the nonlinear Schrödinger equation on surfaces. Invent. Math. 159:187-223.
    • (2005) Invent. Math , vol.159 , pp. 187-223
    • Burq, N.1    Gérard, P.2    Tzvetkov, T.3
  • 9
    • 20444425674 scopus 로고    scopus 로고
    • Multilinear eigenfunction estimates and global existence for the three dimensional nonlinear Schrödinger Equations
    • Burq, N., Gérard, P., Tzvetkov. N. (2005). Multilinear eigenfunction estimates and global existence for the three dimensional nonlinear Schrödinger Equations. Ann. Sci. Ecole Norm. Sup. (4) 38:255-301.
    • (2005) Ann. Sci. Ecole Norm. Sup. (4) , vol.38 , pp. 255-301
    • Burq, N.1    Gérard, P.2    Tzvetkov, N.3
  • 11
    • 0035417541 scopus 로고    scopus 로고
    • Some recent results on the zeros of Bessel functions and orthogonal polynomials
    • Elbert, A. (2001). Some recent results on the zeros of Bessel functions and orthogonal polynomials. J. Comp. Appl. Maths. 133:65-83.
    • (2001) J. Comp. Appl. Maths , vol.133 , pp. 65-83
    • Elbert, A.1
  • 12
    • 0042229265 scopus 로고    scopus 로고
    • Bilinear space-time estimates for homogeneous wave equations
    • Foschi, D., Klainerman, S. (2000). Bilinear space-time estimates for homogeneous wave equations. Ann. Sci. Ecole Norm. Sup. 33:211-274.
    • (2000) Ann. Sci. Ecole Norm. Sup , vol.33 , pp. 211-274
    • Foschi, D.1    Klainerman, S.2
  • 13
    • 54049114289 scopus 로고    scopus 로고
    • Gérard, P., Pierfelice, V. Nonlinear Schrödinger equation on four dimensional compact manifolds. arXiv.org:math/0508116.
    • Gérard, P., Pierfelice, V. Nonlinear Schrödinger equation on four dimensional compact manifolds. arXiv.org:math/0508116.
  • 14
    • 33747492074 scopus 로고    scopus 로고
    • Le problème de Cauchy pour des edp semi-linéaires périodiques en variable d'espace (d'aprés Bourgain) [The Cauchy problem for semilinear PDE with periodic space variables (according to Bourgain)]
    • Ginibre, J. (1996). Le problème de Cauchy pour des edp semi-linéaires périodiques en variable d'espace (d'aprés Bourgain) [The Cauchy problem for semilinear PDE with periodic space variables (according to Bourgain)]. Astérisque 237:163-187.
    • (1996) Astérisque , vol.237 , pp. 163-187
    • Ginibre, J.1
  • 15
    • 85050669204 scopus 로고
    • The global Cauchy problem for the nonlinear Schrödinger equation
    • Ginibre, J., Velo, G. (1985). The global Cauchy problem for the nonlinear Schrödinger equation. Ann. I.H.P. Anal. Non Lin. 2:309-327.
    • (1985) Ann. I.H.P. Anal. Non Lin , vol.2 , pp. 309-327
    • Ginibre, J.1    Velo, G.2
  • 18
    • 0001404168 scopus 로고
    • On nonlinear Schrödinger equations
    • Kato, T. (1987). On nonlinear Schrödinger equations. Ann. I.H.P. Phys. Théor. 46:113-129.
    • (1987) Ann. I.H.P. Phys. Théor , vol.46 , pp. 113-129
    • Kato, T.1
  • 19
    • 0001138601 scopus 로고    scopus 로고
    • Endpoint Strichartz estimates
    • Keel, M., Tao, T. (1998). Endpoint Strichartz estimates. Amer. J. Math. 120:955-980.
    • (1998) Amer. J. Math , vol.120 , pp. 955-980
    • Keel, M.1    Tao, T.2
  • 21
    • 1842535994 scopus 로고    scopus 로고
    • Klainerman, S., Machedon, M. (1996). Remark on Strichartz-type inequalities. (With appendices by J. Bourgain and D. Tataru). Int. Math. Res. Not. 5:201-220.
    • Klainerman, S., Machedon, M. (1996). Remark on Strichartz-type inequalities. (With appendices by J. Bourgain and D. Tataru). Int. Math. Res. Not. 5:201-220.
  • 22
    • 0036383355 scopus 로고    scopus 로고
    • Strichartz estimates for a Schrödinger operator with nonsmooth coefficients
    • Staffilani, G., Tataru, D. (2002). Strichartz estimates for a Schrödinger operator with nonsmooth coefficients. Comm. P.D.E. 27:1337-1372.
    • (2002) Comm. P.D.E , vol.27 , pp. 1337-1372
    • Staffilani, G.1    Tataru, D.2
  • 23
    • 84972553620 scopus 로고
    • Restriction of Fourier transforms to quadratic surfaces and decay of solutions of wave equation
    • Strichartz, R. S. (1977). Restriction of Fourier transforms to quadratic surfaces and decay of solutions of wave equation. Duke Math. J. 44:705-714.
    • (1977) Duke Math. J , vol.44 , pp. 705-714
    • Strichartz, R.S.1
  • 24
    • 0035486554 scopus 로고    scopus 로고
    • Multilinear weighted convolutions of L2 functions and applications to nonlinear dispersive equations
    • Tao, T. (2001). Multilinear weighted convolutions of L2 functions and applications to nonlinear dispersive equations. Amer. J. Math. 123:839-908.
    • (2001) Amer. J. Math , vol.123 , pp. 839-908
    • Tao, T.1
  • 25
    • 38249004799 scopus 로고
    • On global solution to the initial boundary value problem for the nonlinear Schrödinger equation in two space dimensions
    • Tsutsumi, M. (1989). On global solution to the initial boundary value problem for the nonlinear Schrödinger equation in two space dimensions. Nonlin. Anal. T.M.A. 13:1051-1056.
    • (1989) Nonlin. Anal. T.M.A , vol.13 , pp. 1051-1056
    • Tsutsumi, M.1
  • 26
    • 48449103020 scopus 로고    scopus 로고
    • Invariant measures for the nonlinear Schrodinger equation on the disc
    • Tzvetkov, N. (2006). Invariant measures for the nonlinear Schrodinger equation on the disc. Dynamics of PDE 3:111-160.
    • (2006) Dynamics of PDE , vol.3 , pp. 111-160
    • Tzvetkov, N.1
  • 27
    • 0038564013 scopus 로고
    • On the solvability of mixed problem for a nonlinear equation of Schrödinger type
    • Vladimirov, M. V. (1984). On the solvability of mixed problem for a nonlinear equation of Schrödinger type. Sov. Math. Dokl. 29:281-284.
    • (1984) Sov. Math. Dokl , vol.29 , pp. 281-284
    • Vladimirov, M.V.1
  • 28
    • 0000483491 scopus 로고
    • Existence of solutions for Schrödinger evolution equation
    • Yajima, K. (1987). Existence of solutions for Schrödinger evolution equation. Comm. Math. Phys. 110:415-426.
    • (1987) Comm. Math. Phys , vol.110 , pp. 415-426
    • Yajima, K.1


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