Papers and Preprints

Title
Co-authors
Status
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Low regularity conservation laws for integrable PDE R. Killip
X. Zhang
Submitted. math.AP/1708.05362
Almost sure scattering for the energy-critical NLS with radial data below H1(R4) R. Killip
J. Murphy
Submitted. math.AP/1707.09051
The initial-value problem for the cubic-quintic NLS with non-vanishing boundary conditions R. Killip
J. Murphy
Submitted. math.AP/1702.04413
Symplectic non-squeezing for the cubic NLS on the line R. Killip
X. Zhang
To appear in Int. Math. Res. Not. math.AP/1606.09467
Finite-dimensional approximation and non-squeezing for the cubic nonlinear Schrodinger equation on R2 R. Killip
X. Zhang
Submitted. math.AP/1606.07738
Large data mass-subcritical NLS: critical weighted bounds imply scattering R. Killip
S. Masaki
J. Murphy
Nonlinear Differential Equations Appl. 24 (2017), no. 4, Art. 38, 33 pp. math.AP/1606.01512
The focusing cubic NLS with inverse-square potential in three space dimensions R. Killip
J. Murphy
J. Zheng
Differential and Integral Equations 30 (2017), no. 3-4, 161-206. math.AP/1603.08912
The energy-critical NLS with inverse-square potential R. Killip
C. Miao
J. Zhang
J. Zheng
Discrete Contin. Dyn. Syst. 37 (2017), no. 7, 3831-3866. math.AP/1509.05822
Mass-critical inverse Strichartz theorems for 1D Schrodinger operators C. Jao
R. Killip
To appear in Revista Matematica Iberoamericana. math.AP/1509.03592
The final-state problem for the cubic-quintic NLS with non-vanishing boundary conditions R. Killip
J. Murphy
Analysis and PDE 9 (2016), no. 7, 1523-1574. math.AP/1506.06151
Sobolev spaces adapted to the Schrodinger operator with inverse-square potential R. Killip
C. Miao
J. Zhang
J. Zheng
To appear in Mathematische Zeitschrift. math.AP/1503.02716
The focusing cubic NLS in exterior domains in three dimensions R. Killip
X. Zhang
Appl. Math. Res. Express. AMRX (2016), no. 1, 146-180. math.AP/1501.05062
Solitons and scattering for the cubic-quintic nonlinear Schrodinger equation on R3 R. Killip
T. Oh
O. Pocovnicu
Arch. Ration. Mech. Anal. 225 (2017), no. 1, 469-548. math.AP/1409.6734
Scale invariant Strichartz estimates on tori and applications R. Killip Math. Res. Lett. 23 (2016), no. 2, 445-472. math.AP/1409.3603
Quintic NLS in the exterior of a strictly convex obstacle R. Killip
X. Zhang
Amer. J. Math. 138 (2016), no. 5, 1193-1346. math.AP/1208.4904
Riesz transforms outside a convex obstacle R. Killip
X. Zhang
Int. Math. Res. Not. 2016 (2016), no. 19, 5875-5921. math.AP/1205.5784
Blowup behaviour for the nonlinear Klein-Gordon equation R. Killip
B. Stovall
Math. Ann. 358 (2014), no. 1-2, 289-350. math.AP/1203.4886
Global well-posedness of the Gross-Pitaevskii and cubic-quintic nonlinear Schrodinger equations with non-vanishing boundary conditions R. Killip
T. Oh
O. Pocovnicu
Math. Res. Lett. 19 (2012), 969-986. math.AP/1112.1354
Smooth solutions to the nonlinear wave equation can blow up on Cantor sets R. Killip Submitted. math.AP/1103.5257
Global well-posedness and scattering for the defocusing quintic NLS in three dimensions R. Killip Analysis and PDE 5 (2012), 855-885. math.AP/1102.1192
Global well-posedness and scattering for the defocusing cubic NLS in four dimensions Int. Math. Res. Not. 2011 (2011), doi: 10.1093/imrn/rnr051. math.AP/1011.1526
Scattering for the cubic Klein-Gordon equation in two space dimensions R. Killip
B. Stovall
Trans. Amer. Math. Soc. 364 (2012), 1571-1631. math.AP/1008.2712
The radial defocusing energy-supercritical nonlinear wave equation in all space dimensions R. Killip Proc. Amer. Math. Soc. 139 (2011), 1805-1817. math.AP/1002.1756
The defocusing energy-supercritical nonlinear wave equation in three space dimensions R. Killip Trans. Amer. Math. Soc. 363 (2011), 3893-3934. math.AP/1001.1761
On the mass-critical generalized KdV equation R. Killip
S. Kwon
S. Shao
DCDS-A 32 (2012), 191-221. math.AP/0907.5412
Energy-supercritical NLS: critical Hs-bounds imply scattering R. Killip Comm. PDE. 35 (2010), 945-987. math.AP/0812.2084
The characterization of minimal-mass blowup solutions to the focusing mass-critical NLS R. Killip
D. Li
X. Zhang
SIAM J. Math. Anal. 41 (2009), 219-236. math.AP/0804.1124
The focusing energy-critical nonlinear Schrodinger equation in dimensions five and higher R. Killip Amer. J. Math. 132 (2010), 361-424. math.AP/0804.1018
The mass-critical nonlinear Schrodinger equation with radial data in dimensions three and higher R. Killip
X. Zhang
Analysis and PDE 1 (2008), 229-266. math.AP/0708.0849
The cubic nonlinear Schrodinger equation in two dimensions with radial data R. Killip
T. Tao
J. Eur. Math. Soc. 11 (2009), 1203-1258. math.AP/0707.3188
Global existence and scattering for rough solutions to generalized nonlinear Schrodinger equations on R J. Colliander
J. Holmer
X. Zhang
CPAA 7 (2008), 467-489. math.AP/0612452
Energy-critical NLS with quadratic potentials R. Killip
X. Zhang
Comm. PDE. 34 (2009), 1531-1565. math.AP/0611394
Global well-posedness and scattering for the mass-critical nonlinear Schrodinger equation for radial data in high dimensions T. Tao
X. Zhang
Duke Math. J. 140 (2007), 165-202. math.AP/0609692
Minimal-mass blowup solutions of the mass-critical NLS T. Tao
X. Zhang
Forum Math. 20 (2008), 881-919. math.AP/0609690
On the blowup for the $L^2$-critical focusing nonlinear Schrodinger equation in higher dimensions below the energy class X. Zhang SIAM J. Math. Anal. 39 (2007), 34-56. math.AP/0606737
Global well-posedness and scattering for a class of nonlinear Schrodinger equations below the energy space X. Zhang Differential and Integral Equations 22 (2009), 99-124. math.AP/0606611
The defocusing energy-critical nonlinear Schrodinger equation in dimensions five and higher Ph.D. Thesis. pdf file
The Schrodinger equation with combined power-type nonlinearities
T. Tao
X. Zhang
Comm. PDE 32 (2007), 1281-1343.
math.AP/0511070
The defocusing energy-critical nonlinear Schrodinger equation in higher dimensions
Duke Math. J. 138 (2007), 281-374. math.AP/0508298
A counterexample to dispersive estimates for Schrodinger operators in higher dimensions M. Goldberg Comm. Math. Phys. 266 (2006), 211-238. math.AP/0508206
Stability of energy-critical nonlinear Schrodinger equations in high dimensions T. Tao Electron. J. Diff. Eqns. 2005 (2005), 1-28 math.AP/0507005
Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrodinger equation in R^{1+4} E. Ryckman Amer. J. Math. 129 (2007), 1-60. math.AP/0501462