Nonlocal maximum principles for active scalars

DOI10.1016/j.aim.2011.03.019zbMath1244.35022arXiv1009.0542OpenAlexW2963992580MaRDI QIDQ549211

Alexander Kiselev

Publication date: 7 July 2011

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.0542

zbMATH Keywords

maximum principlefluid mechanicsregularity of solutionsactive scalar

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Maximum principles in context of PDEs (35B50) Fractional partial differential equations (35R11)

Related Items (42)

Global well-posedness of slightly supercritical SQG equations and gradient estimate ⋮ Regularity for the supercritical fractional Laplacian with drift ⋮ Global Regularity for a Nonlocal PDE Describing Evolution of Polynomial Roots Under Differentiation ⋮ Long-time asymptotic behavior of the generalized two-dimensional quasi-geostrophic equation ⋮ Local well-posedness for the quasi-geostrophic equations in Besov-Lorentz spaces ⋮ Global regularity for several incompressible fluid models with partial dissipation ⋮ Global regularity for 2D SQG equation with variable viscosity term ⋮ Analyticity and large time behavior for the Burgers equation and the quasi-geostrophic equation, the both with the critical dissipation ⋮ Energy conservation for the generalized surface quasi-geostrophic equation ⋮ Global well-posedness for 2D fractional inhomogeneous Navier–Stokes equations with rough density ⋮ Global smoothness for a 1D supercritical transport model with nonlocal velocity ⋮ Fractional stochastic active scalar equations generalizing the multi-dimensional quasi-geostrophic \& 2D-Navier-Stokes equations: the general case ⋮ Long-time behavior of scalar conservation laws with critical dissipation ⋮ Note on the well-posedness of a slightly supercritical surface quasi-geostrophic equation ⋮ Global regularity for the fractional Euler alignment system ⋮ The 2D Boussinesq equations with logarithmically supercritical velocities ⋮ On the regularity of a class of generalized quasi-geostrophic equations ⋮ On a 1D transport equation with nonlocal velocity and supercritical dissipation ⋮ Global well-posedness for a modified critical dissipative quasi-geostrophic equation ⋮ Singular Cucker–Smale Dynamics ⋮ Absence of anomalous dissipation of energy in forced two dimensional fluid equations ⋮ Self-similar solutions for active scalar equations in Fourier-Besov-Morrey spaces ⋮ On a one-dimensional 𝛼-patch model with nonlocal drift and fractional dissipation ⋮ On the regularity of weak solutions for a modified dissipative quasi-geostrophic equation ⋮ Operator splitting for two-dimensional incompressible fluid equations ⋮ Nonlocal nonlinear advection-diffusion equations ⋮ Global regularity for a 1D Euler-alignment system with misalignment ⋮ Cusp formation for a nonlocal evolution equation ⋮ ON THE WELL-POSEDNESS OF A 2D NONLINEAR AND NONLOCAL SYSTEM ARISING FROM THE DISLOCATION DYNAMICS ⋮ Long time dynamics of forced critical SQG ⋮ Eventual regularity of the two-dimensional Boussinesq equations with supercritical dissipation ⋮ Global smooth solutions to the \(n\)-dimensional damped models of incompressible fluid mechanics with small initial datum ⋮ Regularity results for a class of generalized surface quasi-geostrophic equations ⋮ On a transport equation with nonlocal drift ⋮ On the Hölder regularity of the weak solution to a drift-diffusion system with pressure ⋮ Estimate on the dimension of the singular set of the supercritical surface quasigeostrophic equation ⋮ Long-time solvability for the 2D dispersive SQG equation with improved regularity ⋮ On the Regularity Issues of a Class of Drift-Diffusion Equations with Nonlocal Diffusion ⋮ Decay of solutions to dissipative modified quasi-geostrophic equations ⋮ Lipschitz continuity of solutions to drift-diffusion equations in the presence of nonlocal terms ⋮ On the global regularity for the anisotropic dissipative surface quasi-geostrophic equation ⋮ Global well-posedness, regularity and blow-up for the \(\beta\)-CCF model

Cites Work

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