Critical exponent for evolution equations in modulation spaces

DOI10.1016/j.jmaa.2016.04.051zbMath1339.35033arXiv1411.3115OpenAlexW2230066924MaRDI QIDQ298119

Qiang Huang, Jiecheng Chen, Fan, Dashan

Publication date: 20 June 2016

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.3115

zbMATH Keywords

Cauchy problemfractional heat equation

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Heat equation (35K05) Ill-posed problems for PDEs (35R25) Fractional partial differential equations (35R11)

Related Items (9)

Full characterization of the embedding relations between \(\alpha\)-modulation spaces ⋮ Strongly singular integrals along curves on \(\alpha\)-modulation spaces ⋮ Existence theory for the Boussinesq equation in modulation spaces ⋮ The blow-up solutions for fractional heat equations on torus and Euclidean space ⋮ Boundedness of iterated spherical average on modulation spaces ⋮ Non-integer power estimate in modulation spaces and its applications ⋮ Phase space analysis of the Hermite semigroup and applications to nonlinear global well-posedness ⋮ Time-decay and Strichartz estimates for the BBM equation on modulation spaces: existence of local and global solutions ⋮ Oscillatory hyper-Hilbert transform along curves on modulation spaces

Cites Work

• Asymptotic estimates for unimodular Fourier multipliers on modulation spaces
• Isometric decomposition operators, function spaces \(E_{p,q}^{\lambda}\) and applications to nonlinear evolution equations
• Sharp well-posedness and ill-posedness results for a quadratic nonlinear Schrödinger equation
• The global Cauchy problem for the NLS and NLKG with small rough data
• Unimodular Fourier multipliers for modulation spaces
• Navier-Stokes equations and nonlinear heat equations in modulation spaces with negative derivative indices
• An algebra of pseudodifferential operators
• Well-posedness of the Cauchy problem for the fractional power dissipative equations
• Frequency-uniform decomposition method for the generalized BO, KdV and NLS equations
• The cauchy problem for the critical nonlinear Schrödinger equation in Hs
• Estimates for unimodular Fourier multipliers on modulation spaces
• Modulation Spaces and Nonlinear Evolution Equations
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