Nonlinear dispersive equations

By 小澤徹, 堤誉志雄. 2006

605 citations recorded by the source corpus.

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Citations in the corpus

On Blow-up Solutions to the 3D Cubic Nonlinear Schrödinger Equation (2010, methodology): “It follows from the H local theory optimized by scaling (see Cazenave [3] or Tao [25] for exposition), that if blow-up in finite-time T > 0 occurs, then there is a lower-bound on the “blow-up rate”:”
On the global well-posedness of energy-critical Schr\"odinger equations in curved spaces (2010, background): “In Euclidean spaces, the subcritical theory of such nonlinear Schrödinger equations is well established, see for example the books [18] or [54] for many references.”
Nonlinear Schrodinger Equations at Critical Regularity (2013, background): “It is a form of Gronwall’s inequality that involves both the past and the future, ‘acausal’ in the terminology of [88].”
WIENER RANDOMIZATION ON UNBOUNDED DOMAINS AND AN APPLICATION TO ALMOST SURE WELL-POSEDNESS OF NLS (2014, background): “See [6, 34, 49] for the basic properties of the X-spaces.”
Semilinear Schrödinger flows on hyperbolic spaces: scattering in H1 (2008, background): “6 in [41], it remains to prove the uniform bound (1.”
Linear and Quasi-Linear Evolution Equations in Hilbert Spaces (2012, methodology): “, Majda [108], and Nishida [126]); general relativity, and, specifically, the so-called Einstein vacuum equations (Klainerman and Christodoulou [78], and Klainerman and Nicolò [80]); wave maps (Shatah and Struwe [145], and Tao [156]); von Karman type thin plate equations (Cherrier and Milani [26, 27”
Scattering for the radial 3D cubic wave equation (2014, unknown): “MR 2001m:35200 Zbl 0983.35080 SCATTERING FOR THE RADIAL 3D CUBIC WAVE EQUATION 497 [Tao 2006] T. Tao, Nonlinear dispersive equations: local and global analysis, CBMS Regional Conference Series in Mathematics 106, American Mathematical Society, Providence, RI, 2006.”
On Function Spaces with Mixed Norms — A Survey (2019, background): “More precisely, since the function spaces with mixed norms have finer structures than the corresponding classical function spaces, they naturally arise in the studies on the solutions of partial differential equations used to model physical processes involving in both space and time variables, such ”
Strichartz Estimates in Spherical Coordinates (2012, background): “[32] T. Tao, Spherically averaged endpoint Strichartz estimates for the two-dimensional Schrödinger equation, Commun.”
The focusing energy-critical nonlinear Schr\"odinger equation in dimensions five and higher (2008, background): “It is a form of Gronwall’s inequality that involves both the past and the future, ‘acausal’ in the terminology of [37].”