ON THE MASS-CRITICAL GENERALIZED KDV EQUATION

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We consider the mass-critical generalized Korteweg-de Vries equation (partial derivative(t) + partial derivative(xxx))u = +/-partial derivative(x)(u(5)) for real-valued functions u(t, x). We prove that if the global well-posedness and scattering conjecture for this equation failed, then, conditional on a positive answer to the global well-posedness and scattering conjecture for the mass-critical nonlinear Schrodinger equation (-i partial derivative(t) + partial derivative(xx))u =+/-(vertical bar u vertical bar(4)u), there exists a minimal-mass blowup solution to the mass-critical generalized KdV equation which is almost periodic modulo the symmetries of the equation. Moreover, we can guarantee that this minimal-mass blowup solution is either a self-similar solution, a soliton-like solution, or a double high-to-low frequency cascade solution.
Publisher
AMER INST MATHEMATICAL SCIENCES
Issue Date
2012-01
Language
English
Article Type
Article
Keywords

NONLINEAR SCHRODINGER-EQUATION; GLOBAL WELL-POSEDNESS; RADIAL DATA; BLOW-UP; ROUGH SOLUTIONS; CAUCHY-PROBLEM; DIMENSIONS; SCATTERING; EXISTENCE; COMPACTNESS

Citation

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v.32, no.1, pp.191 - 221

ISSN
1078-0947
DOI
10.3934/dcds.2012.32.191
URI
http://hdl.handle.net/10203/98875
Appears in Collection
MA-Journal Papers(저널논문)
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