Anisotropic estimates for the two-dimensional Kuramoto-Sivashinsky equation

DOI10.1007/s10884-014-9372-3zbMath1342.35140OpenAlexW2009805948WikidataQ115383531 ScholiaQ115383531MaRDI QIDQ481248

Igor Kukavica, Mohammed Ziane, Walter M. Rusin, Saïd Benachour

Publication date: 12 December 2014

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10884-014-9372-3

zbMATH Keywords

Kuramoto-Sivashinsky equationglobal solvabilityanisotropic estimates

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Initial-boundary value problems for higher-order parabolic systems (35K52)

Related Items (14)

Global existence for the two-dimensional Kuramoto-Sivashinsky equation with advection ⋮ Existence and decay of global solutions for the Kuramoto-Sivashinsky-Zakharov-Kuznetsov equation posed on rectangles ⋮ Nonlinear dynamics of a dispersive anisotropic Kuramoto–Sivashinsky equation in two space dimensions ⋮ On the well-posedness of the anisotropically-reduced two-dimensional Kuramoto-Sivashinsky equation ⋮ Regularity criteria for the Kuramoto-Sivashinsky equation in dimensions two and three ⋮ Explicit estimates on the torus for the sup-norm and the crest factor of solutions of the modified Kuramoto-Sivashinky equation in one and two space dimensions ⋮ Existence and decay of global solutions to the three-dimensional Kuramoto-Sivashinsky-Zakharov-Kuznetsov equation ⋮ On the global existence for the Kuramoto-Sivashinsky equation ⋮ Well-posedness of a two-dimensional coordinate-free model for the motion of flame fronts ⋮ Global solutions of the two-dimensional Kuramoto-Sivashinsky equation with a linearly growing mode in each direction ⋮ Global existence for the two-dimensional Kuramoto-Sivashinsky equation with a shear flow ⋮ Global existence and analyticity for the 2D Kuramoto-Sivashinsky equation ⋮ 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
• Unnamed Item
• Backward behavior of solutions of the Kuramoto-Sivashinsky equation
• Navier-Stokes equations with Navier boundary conditions for an oceanic model
• Optimal bounds on the Kuramoto-Sivashinsky equation
• Some global dynamical properties of the Kuramoto-Sivashinsky equations: nonlinear stability and attractors
• Infinite-dimensional dynamical systems in mechanics and physics
• Global analysis of the phase portrait for the Kuramoto-Sivashinsky equation
• Local dissipativity in \(L^2\) for the Kuramoto-Sivashinsky equation in spatial dimension 2
• A global attracting set for the Kuramoto-Sivashinsky equation
• Navier-Stokes equations in three-dimensional thin domains with various boundary conditions
• Large-eigenvalue global existence and regularity results for the Navier-Stokes equation
• Incompressible fluids in thin domains with Navier friction boundary conditions. I.
• A class of solutions of the Navier-Stokes equations with large data
• On Flame Propagation Under Conditions of Stoichiometry
• 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
• New bounds for the Kuramoto‐Sivashinsky equation
• Navier-Stokes Equations on Thin 3D Domains. I: Global Attractors and Global Regularity of Solutions
• A global attracting set for nonlocal Kuramoto–Sivashinsky equations arising in interfacial electrohydrodynamics

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