Lipschitz continuity of solutions to drift-diffusion equations in the presence of nonlocal terms

DOI10.1007/s00021-022-00658-7zbMath1487.35293arXiv2006.01859OpenAlexW4220877141MaRDI QIDQ2078337

Hussain Ibdah

Publication date: 28 February 2022

Published in: Journal of Mathematical Fluid Mechanics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.01859

zbMATH Keywords

maximum principleregularityincompressible Navier-Stokesnon-local drift-diffusion

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Navier-Stokes equations for incompressible viscous fluids (76D05) Fractional derivatives and integrals (26A33) Maximum principles in context of PDEs (35B50) Navier-Stokes equations (35Q30) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Fractional partial differential equations (35R11)

Cites Work

• On nonperiodic Euler flows with Hölder regularity
• Localisation and compactness properties of the Navier-Stokes global regularity problem
• Hölder continuity for a drift-diffusion equation with pressure
• Estimates on fractional higher derivatives of weak solutions for the Navier-Stokes equations
• Dissipative Euler flows and Onsager's conjecture
• Piecewise smooth solutions to the Burgers-Hilbert equation
• Nonlocal maximum principles for active scalars
• Global well-posedness for a modified critical dissipative quasi-geostrophic equation
• Inviscid models generalizing the two-dimensional Euler and the surface quasi-geostrophic equations
• A regularity criterion for the dissipative quasi-geostrophic equations
• Blow up and regularity for fractal Burgers equation
• Lower bounds for an integral involving fractional Laplacians and the generalized Navier-Stokes equations in Besov spaces
• Local estimates on two linear parabolic equations with singular coefficients
• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation in the whole space
• Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation
• Global regularity for a logarithmically supercritical hyperdissipative Navier-Stokes equation
• Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
• On the regularity conditions for the Navier-Stokes and related equations
• Hölder continuity of solutions of supercritical dissipative hydrodynamic transport equations
• Regularity criteria for the dissipative quasi-geostrophic equations in Hölder spaces
• Remarks on the breakdown of smooth solutions for the 3-D Euler equations
• Nonlinear maximum principles for dissipative linear nonlocal operators and applications
• On the loss of continuity for super-critical drift-diffusion equations
• Mild criticality breaking for the Navier-Stokes equations
• Strong solutions to a modified Michelson-Sivashinsky equation
• Navier-Stokes equations and area of interfaces
• Forward self-similar solutions of the fractional Navier-Stokes equations
• Regularity criterion and energy conservation for the supercritical quasi-geostrophic equation
• On fundamental solutions for non-local parabolic equations with divergence free drift
• On the continuity of solutions to advection-diffusion equations with slightly super-critical divergence-free drifts
• Variation on a theme of Caffarelli and Vasseur
• Global well-posedness of slightly supercritical active scalar equations
• Finite time blowup for an averaged three-dimensional Navier-Stokes equation
• Dissipative Models Generalizing the 2D Navier-Stokes and the Surface Quasi-Geostrophic Equations
• Well-posedness for fractional Navier-Stokes equations in the largest critical spaces Ḃ∞,∞−(2β−1)(Rn)
• Enhanced Life Span of Smooth Solutions of a Burgers--Hilbert Equation
• Local formulae for the hydrodynamic pressure and applications
• Global Existence of Weak Solutions for the Burgers--Hilbert Equation
• Singularity formations for a surface wave model
• The Three-Dimensional Navier–Stokes Equations
• Nonlinear Hamiltonian waves with constant frequency and surface waves on vorticity discontinuities
• Regularity of the obstacle problem for a fractional power of the laplace operator
• The Navier-Stokes Problem in the 21st Century
• On the Global Well-Posedness of the Critical Quasi-Geostrophic Equation
• Nonlinear analysis of hydrodynamic instability in laminar flames—I. Derivation of basic equations
• New a priori estimates for navier-stokes equations in dimension 3
• Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids
• Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar
• Hölder estimates for advection fractional-diffusion equations
• On the differentiability of the solution to an equation with drift and fractional diffusion
• Stability and Uniqueness for Piecewise Smooth Solutions to a Nonlocal Scalar Conservation Law with Applications to Burgers--Hilbert Equation
• Shock Formation of the Burgers--Hilbert Equation
• Regularity in Time of Hölder Solutions of Euler and Hypodissipative Navier--Stokes Equations
• Long time solutions for a Burgers-Hilbert equation via a modified energy method
• Singular integrals and periodic functions
• An Eulerian-Lagrangian approach to the Navier-Stokes equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Lipschitz continuity of solutions to drift-diffusion equations in the presence of nonlocal terms