The mass-critical nonlinear Schr\"odinger equation with radial data in dimensions three and higher
暂无分享,去创建一个
[1] R. Killip,et al. The focusing energy-critical nonlinear Schrödinger equation in dimensions five and higher , 2008, 0804.1018.
[2] G. Staffilani,et al. Global Well-Posedness for the $L^2$-critical nonlinear Schr\"odinger equation in higher dimensions , 2006, math/0607632.
[3] Sahbi Keraani,et al. On the blow up phenomenon of the critical nonlinear Schrödinger equation , 2006 .
[4] M. Kwong. Uniqueness of positive solutions of Δu−u+up=0 in Rn , 1989 .
[5] Carlos E. Kenig,et al. Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrödinger equation in the radial case , 2006 .
[6] M. Weinstein,et al. Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation , 1991 .
[7] T. Cazenave,et al. Some remarks on the nonlinear Schrödinger equation in the subcritical case , 1989 .
[8] Terence Tao,et al. The cubic nonlinear Schr\"odinger equation in two dimensions with radial data , 2007, 0707.3188.
[9] J. Bourgain,et al. Refinements of Strichartz' inequality and applications to 2D-NLS with critical nonlinearity , 1998 .
[10] On the role of quadratic oscillations in nonlinear Schrödinger equations , 2002, math/0212171.
[11] Vladimir I. Clue. Harmonic analysis , 2004, 2004 IEEE Electro/Information Technology Conference.
[12] Global well-posedness in Sobolev space implies global existence for weighted L^2 initial data for L^2 -critical NLS , 2005, math/0508001.
[13] Global well-posedness and scattering for the mass-critical nonlinear Schr\"odinger equation for radial data in high dimensions , 2006, math/0609692.
[14] T. Tao. Global regularity of wave maps VI. Abstract theory of minimal-energy blowup solutions , 2009, 0906.2833.
[15] Shuanglin Shao. Sharp linear and bilinear restriction estimates for paraboloids in the cylindrically symmetric case , 2007, 0706.3759.
[16] H. Takaoka,et al. Almost conservation laws and global rough solutions to a Nonlinear Schr , 2002, math/0203218.
[17] M. Weinstein. Nonlinear Schrödinger equations and sharp interpolation estimates , 1983 .
[18] N. Tzirakis. The Cauchy problem for the semilinear quintic Schr , 2002, math-ph/0212061.
[19] F. Merle,et al. Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power , 1993 .
[20] Pascal B'egout,et al. Mass concentration phenomena for the $L^2$-critical nonlinear Schrödinger equation , 2007, 1207.2028.
[21] M. Grillakis,et al. ON THE GLOBAL EXISTENCE OF ROUGH SOLUTIONS OF THE CUBIC DEFOCUSING SCHRÖDINGER EQUATION IN R2 + 1 , 2007 .
[22] YeYaojun. GLOBAL SOLUTIONS OF NONLINEAR SCHRODINGER EQUATIONS , 2005 .
[23] G. Staffilani. On the generalized Korteweg-de Vries-type equations , 1997, Differential and Integral Equations.
[24] Y. Tsutsumi. Scattering problem for nonlinear Schrödinger equations , 1985 .
[25] Global well-posedness and scattering for the energy-critical nonlinear Schr\"odinger equation in R^3 , 2004, math/0402129.
[26] T. Tao,et al. Resonant decompositions and the $I$-method for the cubic nonlinear Schrödinger equation on $\mathbb{R}^2$ , 2008 .
[27] M. Visan. The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions , 2005, math/0508298.
[28] Terence Tao,et al. Global well-posedness and scattering for the defocusing mass-critical nonlinear Schrödinger equation for radial data in high dimensions , 2007 .
[29] J. Ginibre,et al. Smoothing properties and retarded estimates for some dispersive evolution equations , 1992 .
[30] M. Visan,et al. Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4 , 2007 .
[31] T. Tao,et al. Resonant decompositions and the I-method for cubic nonlinear Schrodinger on R^2 , 2007, 0704.2730.
[32] M. Grillakis,et al. Improved interaction Morawetz inequalities for the cubic nonlinear Schr , 2007, math/0703606.
[33] H. Helson. Harmonic Analysis , 1983 .
[34] H Berestycki,et al. EXISTENCE D'ONDES SOLITAIRES DANS DES PROBLEMES NON LINEAIRES DU TYPE KLEIN-GORDON , 1979 .
[35] Tosio Kato. On nonlinear Schrödinger equations, II.HS-solutions and unconditional well-posedness , 1995 .
[36] T. Cazenave. Semilinear Schrodinger Equations , 2003 .
[37] T. Tao. Global regularity of wave maps III. Large energy from $\R^{1+2}$ to hyperbolic spaces , 2008, 0805.4666.
[38] I. M. Pyshik,et al. Table of integrals, series, and products , 1965 .
[39] Yoshio Tsutsumi,et al. L2 concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power nonlinearity , 1990 .
[40] J. Bourgain. Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case , 1999 .
[41] T. Tao,et al. Endpoint Strichartz estimates , 1998 .
[42] Remi Carles. CRITICAL NONLINEAR SCHRÖDINGER EQUATIONS WITH AND WITHOUT HARMONIC POTENTIAL , 2001 .
[43] R. Carles,et al. On the role of quadratic oscillations in nonlinear Schrödinger equations II. The $L^2$-critical case. , 2002, math/0212171.
[44] Hayato Nawa,et al. ASYMPTOTIC AND LIMITING PROFILES OF BLOWUP SOLUTIONS OF THE NONLINEAR SCHRODINGER EQUATION WITH CRITICAL POWER , 1999 .
[45] G. Staffilani,et al. Global Well-Posedness and Polynomial Bounds for the Defocusing L 2-Critical Nonlinear Schrödinger Equation in ℝ , 2008 .
[46] E. Stein,et al. Introduction to Fourier Analysis on Euclidean Spaces. , 1971 .
[47] F. Merle,et al. Compactness at blow-up time for L2 solutions of the critical nonlinear Schrödinger equation in 2D , 1998 .
[48] Terence Tao,et al. Minimal-mass blowup solutions of the mass-critical NLS , 2006, math/0609690.
[49] F. Merle,et al. Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation , 2006, math/0610801.
[50] T. Tao. A pseudoconformal compactification of the nonlinear Schrodinger equation and applications , 2006, math/0606254.
[51] T. Tao. Global regularity of wave maps IV. Absence of stationary or self-similar solutions in the energy class , 2008, 0806.3592.
[52] Xiaoyi Zhang,et al. On the Blowup for the L2-Critical Focusing Nonlinear Schrödinger Equation in Higher Dimensions below the Energy Class , 2007, SIAM J. Math. Anal..
[53] S. Keraani. On the Defect of Compactness for the Strichartz Estimates of the Schrödinger Equations , 2001 .
[54] I. S. Gradshteyn,et al. Table of Integrals, Series, and Products , 1976 .
[55] Ground state mass concentration in the L^2-critical nonlinear Schrodinger equation below H^1 , 2004, math/0409585.
[56] Robert S. Strichartz,et al. Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations , 1977 .
[57] Global well-posedness and scattering for the higher-dimensional energy-critical non-linear Schrodinger equation for radial data , 2004, math/0402130.