Decay of solutions to dissipative modified quasi-geostrophic equations

DOI10.1090/proc/13280zbMath1353.35060OpenAlexW2404079634MaRDI QIDQ2832828

César J. Niche, Gabriela Planas, Lucas C. F. Ferreira

Publication date: 14 November 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc/13280

zbMATH Keywords

Fourier splitting methodfractional diffusionactive scalar equationtime-polynomial decay

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) PDEs in connection with geophysics (35Q86)

Related Items (12)

Long-time asymptotic behavior of the generalized two-dimensional quasi-geostrophic equation ⋮ Analyticity and large time behavior for the Burgers equation and the quasi-geostrophic equation, the both with the critical dissipation ⋮ Decay character and the semilinear structurally damped \(\sigma\)-evolution equations ⋮ Long-time behavior of global solutions of anisotropic quasi-geostrophic equations in Sobolev space ⋮ Decay rates for the 4D energy‐critical nonlinear heat equation ⋮ Upper and lower \(\dot{H}^m\) estimates for solutions to parabolic equations ⋮ Decay character and estimates for the damped wave equation ⋮ Optimal convergence rates of the supercritical surface quasi-geostrophic equation ⋮ On the forced surface quasi-geostrophic equation: existence of steady states and sharp relaxation rates ⋮ Upper and lower bounds of decay rates for \(\dot{H}^{- \frac{1}{2}}\) weak solutions of the surface quasi-geostrophic equation ⋮ Lower bounds on mixing norms for the advection diffusion equation in \(\mathbb{R}^d\) ⋮ Sharp decay estimates and asymptotic behaviour for 3D magneto-micropolar fluids

Cites Work

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• Weak-strong uniqueness criterion for the \(\beta\)-generalized surface quasi-geostrophic equation
• Existence and decay of solutions to the dissipative quasi-geostrophic equation with delays
• Nonlocal maximum principles for active scalars
• Global well-posedness for a modified dissipative surface quasi-geostrophic equation in the critical Sobolev space \(H^{1}\)
• On the regularity of a class of generalized quasi-geostrophic equations
• Global well-posedness for a modified critical dissipative quasi-geostrophic equation
• Global well-posedness and symmetries for dissipative active scalar equations with positive-order couplings
• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• On the Serrin's regularity criterion for the \(\beta\)-generalized dissipative surface quasi-geostrophic equation
• Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
• Poincaré's inequality and diffusive evolution equations
• \(L^ 2\) decay for weak solutions of the Navier-Stokes equations
• Optimal smoothing and decay estimates for viscously damped conservation laws, with applications to the 2-D Navier-Stokes equation
• Decay of weak solutions to the 2D dissipative quasi-geostrophic equation
• Characterization of Solutions to Dissipative Systems with Sharp Algebraic Decay
• Dissipative Models Generalizing the 2D Navier-Stokes and the Surface Quasi-Geostrophic Equations
• The asymptotic behaviour of subcritical dissipative quasi-geostrophic equations
• Regularity and Blow up for Active Scalars
• Global regularity for a modified critical dissipative quasi-geostrophic equation
• Large time behaviour of solutions to the navier-stokes equations
• Decay Results for Weak Solutions of the Navier-Stokes Equations on Rⁿ
• Decay of solution to parabolic conservation laws
• Behavior of Solutions of 2D Quasi-Geostrophic Equations
• Partial regularity of suitable weak solutions of the navier-stokes equations
• Decay characterization of solutions to dissipative equations

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