Optimal bounds on the Kuramoto-Sivashinsky equation

DOI10.1016/j.jfa.2009.01.034zbMath1194.35082OpenAlexW2027854577MaRDI QIDQ837077

Felix Otto

Publication date: 10 September 2009

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2009.01.034

zbMATH Keywords

periodic boundary conditionsLittlewood-Paley decompositionBurgers equation with sourceOleinik's estimatezero mean value

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for higher-order parabolic equations (35K35) A priori estimates in context of PDEs (35B45) Semilinear parabolic equations (35K58) Harmonic analysis and PDEs (42B37)

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Cites Work

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• Inertial manifolds for the Kuramoto-Sivashinsky equation and an estimate of their lowest dimension
• Convergence of approximate solutions to conservation laws
• Some global dynamical properties of the Kuramoto-Sivashinsky equations: nonlinear stability and attractors
• Steady solutions of the Kuramoto-Sivashinsky equation
• Analyticity for the Kuramoto-Sivashinsky equation
• Dissipativity, analyticity and viscous shocks in the (de)stabilized Kuramoto-Sivashinsky equation
• A global attracting set for the Kuramoto-Sivashinsky equation
• Uncertainty estimates andL₂bounds for the Kuramoto–Sivashinsky equation
• Stability of the kuramoto‐sivashinsky and related systems
• New bounds for the Kuramoto‐Sivashinsky equation
• Minimal entropy conditions for Burgers equation

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