On self-similar singular solutions of the complex Ginzburg-Landau equation

DOI10.1002/cpa.3006zbMath1032.35162arXivmath/0007149OpenAlexW1935391009MaRDI QIDQ4790253

Vladimír Šverák, Petr Plecháč

Publication date: 28 January 2003

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0007149

zbMATH Keywords

stabilitysingularitiescomplex Ginzburg-Landau equationsupercritical nonlinear Schrödinger equationself-similar singularities

Mathematics Subject Classification ID

Analyticity in context of PDEs (35A20) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40)

Related Items (15)

Global regularity for a model of Navier-Stokes equations with logarithmic sub-dissipation ⋮ Construction of Blowup Solutions for the Complex Ginzburg-Landau Equation with Critical Parameters ⋮ Refined asymptotics for the blow-up solution of the complex Ginzburg-Landau equation in the subcritical case ⋮ Existence and stability of spatial plane waves for the incompressible Navier-Stokes in \(\mathbb R^3\) ⋮ Blow-up profile for the complex Ginzburg-Landau equation ⋮ Construction of a blow-up solution for the complex Ginzburg-Landau equation in a critical case ⋮ Asymptotic analysis of a new type of multi-bump, self-similar, blowup solutions of the Ginzburg–Landau equation ⋮ A Liouville theorem for vector valued semilinear heat equations with no gradient structure and applications to blow-up ⋮ Multi-bump, self-similar, blow-up solutions of the Ginzburg-Landau equation ⋮ Self-similar blow-up profiles for slightly supercritical nonlinear Schrödinger equations ⋮ Finite time blowup for an averaged three-dimensional Navier-Stokes equation ⋮ Pathfollowing for essentially singular boundary value problems with application to the complex Ginzburg-Landau equation ⋮ Blow-up for a semi-linear advection-diffusion system with energy conservation ⋮ Are the incompressible 3d Navier-Stokes equations locally ill-posed in the natural energy space? ⋮ On singularities in the quaternionic Burgers equation

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• On Leray's self-similar solutions of the Navier-Stokes equations
• Partial Regularity of Suitable Weak Solutions of Complex Ginzburg Landau Equations
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