Nonlinear dispersive equations : local and global analysis

By Terence Tao. 2006

1,826 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/68bced8247ec3a76b51418e479448ca602c05884

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In Mathematical Physics

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Citations in the corpus

Strichartz Estimates in Spherical Coordinates (2012, background): “x)dx. There has been a lot of work on the space time estimates for the solution u which play important roles in recent studies on nonlinear dispersive equations. (See Cazenave [5], Sogge [28] and Tao [34] and references therein.) Especially, when ω(ρ) = ρa, a 6= 0, the solution satisﬁes (1.2) kukLq ”
Asymptotic stability of solitons for mKdV (2015, positive): “liton with exponential decay as x→ +∞. This result was then reﬁned 2For more on the local and global well-posedness and ill-posedness of KdV and generalized KdV equations we refer to the books of Tao [49] and Linares-Ponce [34]. 3Similarly to how it is stated in Theorem 3.1. ASYMPTOTIC STABILITY OF ”
On Blow-up Solutions to the 3D Cubic Nonlinear Schrödinger Equation (2010, methodology): “Denote by I = (−T∗, T ∗) the maximal interval of existence of the solution u (e.g., see [ 3 ]).”
Invariant Measures and Long-Time Behavior for the Benjamin–Ono Equation (2014, background): “Properties (1)–(4) are well-known properties of Xs,b spaces, see [24].”
Global regularity of wave maps III. Large energy from $\R^{1+2}$ to hyperbolic spaces (2008, background): “which solutions at the critical regularity can be constructed by iteration, results such as Claim 1.10 are standard consequences of the function space estimates used in the iteration scheme; see e.g. [65]. Remark 1.12. The author does not claim that these maximal Cauchy developments solve the wave m”