Global solutions of the two-dimensional Kuramoto-Sivashinsky equation with a linearly growing mode in each direction

DOI10.1007/s00332-021-09748-8zbMath1476.35035arXiv2102.05093OpenAlexW3204795010MaRDI QIDQ2239310

Anna L. Mazzucato, David M. Ambrose

Publication date: 3 November 2021

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.05093

zbMATH Keywords

Lyapunov functionglobal existenceperiodic boundary conditionshigh wave numbersintermediate wave numberslow wave numbers

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for higher-order parabolic equations (35K35) Semilinear parabolic equations (35K58)

Related Items

Homogenization theory: periodic and beyond. Abstracts from the workshop held March 14--20, 2021 (online meeting) ⋮ Regularity criteria for the Kuramoto-Sivashinsky equation in dimensions two and three ⋮ Well-posedness of a two-dimensional coordinate-free model for the motion of flame fronts ⋮ Global existence for the two-dimensional Kuramoto-Sivashinsky equation with a shear flow ⋮ Dissipation enhancement of planar helical flows and applications to three-dimensional Kuramoto-Sivashinsky and Keller-Segel equations ⋮ Well-Posedness and Asymptotics of a Coordinate-Free Model of Flame Fronts

Cites Work

• Unnamed Item
• Small strong solutions for time-dependent mean field games with local coupling
• Anisotropic estimates for the two-dimensional Kuramoto-Sivashinsky equation
• Dissipation length scale estimates for turbulent flows: a Wiener algebra approach
• Optimal bounds on the Kuramoto-Sivashinsky equation
• On the equation of a curved flame front
• Partial differential equations. III: Nonlinear equations.
• Existence and generalized Gevrey regularity of solutions to the Kuramoto-Sivashinsky equation in \(\mathbb R^n\)
• Some global dynamical properties of the Kuramoto-Sivashinsky equations: nonlinear stability and attractors
• Global vortex sheet solutions of Euler equations in the plane
• Nonlinear stability and dynamical properties for a Kuramoto-Sivashinsky equation in space dimension two
• Nonlinear stability and optimal decay rate for a multidimensional generalized Kuramoto-Sivashinsky system
• Local dissipativity in \(L^2\) for the Kuramoto-Sivashinsky equation in spatial dimension 2
• Strong solutions for time-dependent mean field games with non-separable Hamiltonians
• On the well-posedness of an anisotropically-reduced two-dimensional Kuramoto-Sivashinsky equation
• Global existence and analyticity for the 2D Kuramoto-Sivashinsky equation
• Temporal boundary value problems in interfacial fluid dynamics
• Uncertainty estimates andL₂bounds for the Kuramoto–Sivashinsky equation
• New Bounds for the Inhomogenous Burgers and the Kuramoto-Sivashinsky Equations
• The Well-Posedness of the Kuramoto–Sivashinsky Equation
• Nonlinear analysis of hydrodynamic instability in laminar flames—I. Derivation of basic equations
• Local dissipativity and attractors for the Kuramoto-Sivashinsky equation in thin 2D domains
• Stability of the kuramoto‐sivashinsky and related systems
• Finite-time singularity versus global regularity for hyper-viscous Hamilton–Jacobi-like equations
• A bounded global absorbing set for the Burgers–Sivashinsky equation in space dimension two
• Nonlinear dynamics of a dispersive anisotropic Kuramoto–Sivashinsky equation in two space dimensions
• Large dispersion, averaging and attractors: three 1D paradigms
• New bounds for the Kuramoto‐Sivashinsky equation
• Global solutions and ill-posedness for the Kaup system and related Boussinesq systems
• EFFICIENT COMPUTATION OF COORDINATE-FREE MODELS OF FLAME FRONTS
• The radius of analyticity for solutions to a problem in epitaxial growth on the torus
• An in-depth numerical study of the two-dimensional Kuramoto–Sivashinsky equation

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