Frequency-uniform decomposition, function spaces \(X^s_{p, q}\), and applications to nonlinear evolution equations

DOI10.1155/2013/176596zbMath1279.46022OpenAlexW2027572566WikidataQ59013619 ScholiaQ59013619MaRDI QIDQ2392168

Jiecheng Chen, Shaolei Ru

Publication date: 1 August 2013

Published in: Journal of Function Spaces and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2013/176596

zbMATH Keywords

Cauchy problemfunction spacefrequency-uniform decomposition

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) NLS equations (nonlinear Schrödinger equations) (35Q55) Ginzburg-Landau equations (35Q56)

Cites Work

• Nonlinear small data scattering for the wave and Klein-Gordon equation
• Isometric decomposition operators, function spaces \(E_{p,q}^{\lambda}\) and applications to nonlinear evolution equations
• The global Cauchy problem for the NLS and NLKG with small rough data
• Theory of function spaces
• Global well-posedness and scattering for the derivative nonlinear Schrödinger equation with small rough data
• Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
• Nonlinear Schrödinger equations in the Sobolev space of critical order
• A note on Tauberian theorems
• On nonlinear Schrödinger equations. II: \(H^ S\)-solutions and unconditional well-posedness
• Frequency-uniform decomposition method for the generalized BO, KdV and NLS equations
• The cauchy problem for the critical nonlinear Schrödinger equation in Hs
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