Title | With | Status | Download |
Amer. J. Math., 120 (1998), 955-980 | |||
Comm. PDE 24 (1999), 599—630 | |||
Amer. J. Math. 121 (1999), 629-669 | |||
Local and global well-posedness of wave maps in R^{1+1} for rough data | IMRN 21 (1998), 1117-1156 | arXiv:9807171 | |
Spherically averaged endpoint Strichartz estimates for the two-dimensional Schrödinger equation | Comm. PDE 25 (2000), 1471-1485 | arXiv:9811168 | |
Ill-posedness for one-dimensional wave maps at the critical regularity | Amer. J. Math., 122 (2000), 451-463 | arXiv:9811169 | |
Local well-posedness for the Yang-Mills equation below the energy norm |
| JDE 189 (2003), 366-382 | arXiv:0005064 |
Almost conservation laws and global rough solutions to a nonlinear Schrodinger equation | Hideo Takaoka | Math. Res. Letters 9 (2002), 659-682. | arXiv:0203218 |
| Amer. J. Math. 123 (2001), 839-908 | arXiv:0005001 | |
Global well-posedness result for KdV in Sobolev spaces of negative index | Hideo Takaoka | EJDE 2001 (2001) No 26, 1-7 | arXiv:0101261 |
Sharp global well-posedness results for periodic and non-periodic KdV and modified KdV on R and T | Hideo Takaoka | J. Amer. Math. Soc. 16 (2003), 705-749. | arXiv:0110045 |
Multi-linear estimates for periodic KdV equations, and applications | Hideo Takaoka | J. Funct. Anal. 211 (2004), 173-218 | arXiv:0110049 |
Global well-posedness for the Schrodinger equations with derivative | Hideo Takaoka | Siam J. Math. 33 (2001), 649-669 | arXiv:0101263 |
Global regularity of wave maps I. Small critical Sobolev norm in high dimension |
| IMRN 7 (2001), 299-328 | arXiv:0010068 |
Global regularity of wave maps II. Small energy in two dimensions |
| Comm. Math. Phys. 224 (2001), 443-544 | arXiv:0011173 |
A refined global well-posedness for the Schrodinger equations with derivative | Hideo Takaoka | Siam J. Math. 34 (2002), 64-86. | arXiv:0110026 |
Resonant decompositions and the I-method for cubic nonlinear Schrodinger on R^2 | Hideo Takaoka | Disc. Cont. Dynam. Systems A 21 (2008), 665-686 | |
Polynomial upper bounds for the orbital instability of the 1D cubic NLS below the energy norm | Hideo Takaoka | Discrete Cont. Dynam. Systems 9 (2003), 31-54 | arXiv:0206218 |
Polynomial growth and orbital instability bounds for $L^2$-subcritical NLS below the energy norm | Hideo Takaoka | Comm. Pure Appl. Anal. 2 (2003), 33-50 | arXiv:0212113 |
Global existence and scattering for rough solutions of a nonlinear Schrodinger equation in R^3 | Hideo Takaoka | CPAM 57 (2004), 987-1014 | arXiv:0301260 |
A physical approach to wave equation bilinear estimates | J. Anal. Math. 87 (2002), 299—336 | arXiv:0106091 | |
A singularity removal theorem for Yang-Mills fields in higher dimensions | J. Amer. Math. Soc. 17 (2004), 557-593. | arXiv:0209352 | |
Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocussing equations | Amer. J. Math. 125 (2003), 1235-1293 | arXiv:0203044 | |
Global regularity for the Maxwell-Klein-Gordon equation in high dimensions | Comm. Math. Phys. 251 (2004), 377-426 | arXiv:0309353 | |
Symplectic nonsqueezing of the KdV flow | Hideo Takaoka | Acta Math. 195 (2005), 197-252 | arXiv:0412381 |
Upper and lower bounds for Dirichlet eigenfunctions | Math. Res. Letters 9 (2002), 289-305 | arXiv:0202140 | |
Ill-posedness for nonlinear Schrodinger and wave equations | Unpublished preprint | arXiv:0311048 | |
Local and global well-posedness for nonlinear dispersive equations |
| Proc. Centre Math. Appl. Austral. Nat. Univ. 40 (2002), 19-48 | |
Hideo Takaoka | Journées "Équations aux Dérivées Partielles" (Forges-les-Eaux, 2002), Exp. No. X, 14 pp., Univ. Nantes, Nantes,2002 | ||
Global well-posedness and scattering in the energy space for the critical nonlinear Schrodinger equation in R^3 ("Project Gopher") | Hideo Takaoka | Annals of Math. 167 (2007), 767-865 [A survey article is in Contemp. Math. 439, "Recent Developments in Nonlinear Partial Differential Equations: The second symposium on Analysis and PDEs June 7-10 2004, Purdue University, West Lafayette Indiana", D. Danielli, Ed., pp. 69-80. American Mathematial Society, Providence RI 2007] | arXiv:0402129 |
Long-time decay estimates for Schrodinger equations on manifolds | Mathematical aspects of nonlinear dispersive equations, 223-253, Ann. of Math. Stud. 163, Princeton University Press, Princeton NJ 2007 | arXiv:0412416 | |
A Strichartz inequality for the Schrodinger equation on non-trapping asymptotically conic manifolds | Comm. PDE 30 (2004), 157-205 | arXiv:0312225 | |
Global well-posedness of the Benjamin-Ono equation in H^1(R) |
| J. Hyperbolic Diff. Eq. 1 (2004) 27-49 | arXiv:0307289 |
Instability of the periodic nonlinear Schrodinger equation | Unpublished preprint | arXiv:0311227 | |
On the asymptotic behavior of large radial data for a focusing non-linear Schr\"odinger equation |
| Dynamics of PDE 1 (2004), 1-48 | arXiv:0309428 |
Global well-posedness and scattering for the higher-dimensional energy-critical non-linear Schrodinger equation for radial data |
| New York Journal of Mathematics 11 (2005), 57-80 | arXiv:0402130 |
Sharp Strichartz estimates on non-trapping asymptotically conic manifolds | Amer. J. Math. 128 (2006), 963—1024. | arXiv:0408273 | |
Geometric renormalization of large energy wave maps |
| Journees “Equations aux derives partielles”, Forges les Eaux, 7-11 June 2004, XI 1-32 | arXiv:0411354 |
Stability of energy-critical nonlinear Schr\"odinger equations in high dimensions | Electron. J. Diff. Eq. Vol. 2005 (2005), No. 118, 1-28. | arXiv:0507005 | |
Sharp well-posedness and ill-posedness results for a quadratic non-linear Schr\"odinger equation | Ioan Bejenaru | J. Funct. Anal. Vol. 233 (2006), 228-259 | arXiv:0508210 |
Velocity averaging, kinetic formulations, and regularizing effects in quasilinear PDE. | CPAM 61 (2007), 1-34 | arXiv:0511054 | |
The nonlinear Schr\”odinger equation with combined power-type nonlinearities | Xiaoyi Zhang | Comm. PDE 32 (2007), 1281-1343. | arXiv:0511070 |
Spacetime bounds for the energy-critical nonlinear wave equation in three spatial dimensions |
| Dynamics of PDE 3 (2006), 93-110 | arXiv:0601164 |
Scattering for the quartic generalised Korteweg-de Vries equation |
| J. Diff. Eq. 232 (2007), 623—651 | arXiv:0605357 |
Global regularity for a logarithmically supercritical defocusing nonlinear wave equation for spherically symmetric data |
| J. Hyperbolic Diff. Eq. 4 (2007), 259-266 | arXiv:0606145 |
Two remarks on the generalised Korteweg-de Vries equation |
| Discrete Cont. Dynam. Systems 18 (2007), 1-14 | arXiv:0606236 |
A pseudoconformal compactification of the nonlinear Schrodinger equation and applications |
| New York J. Math. 15 (2009), 265--282. | arXiv:0606254 |
Global behaviour of nonlinear dispersive and wave equations |
| Current Developments in Mathematics 2006, International Press. 255-340. | arXiv:0608293 |
Minimal-mass blowup solutions of the mass-critical NLS | Xiaoyi Zhang | Forum Mathematicum 20 (2008), 881-919 | |
Global well-posedness and scattering for the mass-critical nonlinear Schr\”odinger equation for radial data in high dimensions | Xiaoyi Zhang | Duke Math J. 140 (2007), 165-202 | |
A counterexample to an endpoint bilinear Strichartz inequality |
| Electron. J. Diff. Eq. 2006 (2006) 151, 1—6. | |
A (concentration-)compact attractor for high-dimensional non-linear Schrödinger equations |
| Dynamics of PDE 4 (2007), 1-53 | |
A priori bounds and weak solutions for the nonlinear Schrödinger equation in Sobolev spaces of negative order | J. Funct. Anal 254 (2007), 368-395 | ||
The cubic nonlinear Schrödinger equation in two dimensions with radial data | J. Eur. Math. Soc. (JEMS) 11 (2009), no. 6, 1203--1258. | ||
A quantitative formulation of the global regularity problem for the periodic Navier-Stokes equation | Dynamics of PDE 4 (2007), 293--302. | ||
Why are solitons stable? | Bull. Amer. Math. Soc. 46 (2009), 1-33. | ||
A global compact attractor for high-dimensional defocusing non-linear Schrödinger equations with potential | Dynamics of PDE 5 (2008), 101—116. | ||
Global regularity of wave maps III. Large energy from $R^{1+2}$ to hyperbolic spaces. ("Project Heatwave", part 1 of 5.) | Unpublished preprint | ||
Global regularity of wave maps IV. Absence of stationary or self-similar solutions in the energy class ("Project Heatwave", part 2 of 5.) | Unpublished preprint | ||
Global existence and uniqueness results for weak solutions of the focusing mass-critical non-linear Schrödinger equation | Anal. PDE 2 (2009), no. 1, 61--81. | ||
Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrodinger equation | Hideo Takaoka | Inventiones Math.181 (2010), 39-113 | |
Global regularity of wave maps V. Large data local well-posedness in the energy class ("Project Heatwave", part 3 of 5.) |
| Unpublished preprint | |
The high exponent limit p \to \infty for the one-dimensional nonlinear wave equation |
| Anal. PDE 2 (2009), no. 2, 235--259. | |
An inverse theorem for the bilinear L^2 Strichartz estimate for the wave equation |
| Unpublished preprint | |
Global regularity of wave maps VI. Abstract theory of minimal-energy blowup solutions (“Project Heatwave”, part 4 of 5.) |
| Unpublished preprint | |
Global regularity of wave maps VII. Control of delocalised or dispersed solutions (“Project Heatwave”, part 5 of 5.) |
| Unpublished preprint | |
Global regularity for a logarithmically supercritical hyperdissipative Navier-Stokes equation |
| Analysis & PDE 2 (2009), 361-366 | |
Operator splitting for the KdV equation | Math. Comp. 80 (2011) 821-846. | ||
Global well-posedness for the Maxwell-Klein-Gordon equation below the energy norm | |||
Asymptotic decay for a one-dimensional nonlinear wave equation | Hans Lindblad | ||
Effective limiting absorption principles, and applications | Comm. Math. Phys. 333 (2015), 1-95 | ||
Localisation and compactness properties of the Navier-Stokes global regularity problem | |||
Concentration compactness for critical wave maps, by Joachim Krieger and Wilhelm Schlag | Bull. Amer. Math. Soc. 50 (2013), 655-662 | ||
Finite time blowup for an averaged three-dimensional Navier-Stokes equation | J. Amer. Math. Soc. 29 (2016), no. 3, 601–674. | ||
Why global regularity for Navier-Stokes is hard (translated, Chinese) | "Mathematical Advances in Translation", vol. 33, No.3. p.212-221. | ||
Finite time blowup for a supercritical defocusing nonlinear wave system | Anal. PDE 9 (2016), no. 8, 1999–2030. | ||
Finite time blowup for a high dimensional nonlinear wave systems with bounded smooth nonlinearity | Comm. Partial Differential Equations 41 (2016), no. 8, 1204–1229. | ||
Finite time blowup for Lagrangian modifications of the three-dimensional Euler equation | Ann. PDE 2 (2016), no. 2, Art. 9, 79 pp. | ||
Finite time blowup for a supercritical defocusing nonlinear Schr\"odinger system | Analysis & PDE 11-2 (2018), 383--438. DOI 10.2140/apde.2018.11.383 | ||
On the universality of potential well dynamics | Dynamics of PDE 14 (2017), 219--238. | ||
On the universality of the incompressible Euler equation on compact manifolds | Disc. Cont. Dynam. Sys. 38 (2018), 1553-1565 | ||
On the universality of the incompressible Euler equation on compact manifolds, II. Non-rigidity of Euler flows | Pure Appl. Funct. Anal. 5 (2020), no. 6, 1425–1443. | ||
Searching for singularities in the Navier–Stokes equations | Nature Reviews Physics 1, 418–419(2019) | ||
Quantitative bounds for critically bounded solutions to the Navier-Stokes equations | Nine mathematical challenges—an elucidation, 149–193, Proc. Sympos. Pure Math., 104, Amer. Math. Soc., Providence, RI, [2021], ©2021. |
Some further PDE-related preprints can be found in my Kakeya/restriction preprints page.
Back to my preprints page.
