The global Cauchy problem for the NLS and NLKG with small rough data

By Baoxiang Wang, Henryk Hudzik. 2007

270 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f41739352186109294b6a9a62877f1a87e5835c1

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In Applied Mathematics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Frequency-uniform decomposition method for the generalized BO, KdV and NLS equations (2007, methodology): “Wang and Hudzik [40] generalized their embeddings to the cases 0 < p,q ∞.”
Decay estimates for a class of wave equations (2008, background): “If κ ≥ 4/n, the global well posedness and the scattering with small data in Hs were studied in [10, 11, 14, 18, 19, 21].”
Remarks on Fourier multipliers and applications to the Wave equation (2008, background): “This was first considered, for the modulation spaces, in [1, 3, 14, 15], where the classical framework of L, Sobolev or Besov spaces is abandoned in favour of such spaces, which permit to handle initial data which are not covered by the classical results.”
Navier–Stokes equations and nonlinear heat equations in modulation spaces with negative derivative indices (2010, methodology): “To state our theorems, we introduce the following function spaces l (L r(0, T ; Lq(Rn))) which were introduced by Wang and Hudzik [19].”
Global well-posedness and scattering for the derivative nonlinear Schrödinger equation with small rough data (2009, background): “[31]) ∥∥F−1 ξ̄ eit |ξ̄ 2±ηk̄(ξ̄ ) ∥∥ L∞̄x (Rn−1) ( 1 + |t |)−(n−1)/2, ∥∥F−1 ξ1 eitξ2 1 ηk1(ξ1)∥∥L∞x1 (R) (1 + |t |)−1/2.”
The inclusion relation between Sobolev and modulation spaces (2010, methodology): “Modulation spaces are also used as a regularity class of initial data of the Cauchy problem for nonlinear evolution equations, and in this way the existence of the solution is shown under very low regularity assumption for initial data (see [21], [22], [23]).”
α-modulation spaces (I) scaling, embedding and algebraic properties (2014, background): “1 Duality It is known that the dual space of Besov space Bs p,q is B −s+n(1/(p∧1)−1) (p∨1)∗,(q∨1)∗ (see [18]) and the dual space of modulation space M s p,q is M −s (p∨1)∗,(q∨1)∗ (see [19]).”
Sharpness of some properties of Wiener amalgam and modulation spaces (2008, unknown): “As an example, in Section 4 we prove the optimality of an estimate for the Schrödinger propagator, recently obtained in [22] (see also [1]).”