Suppression of Blow-Up in Patlak--Keller--Segel Via Shear Flows

DOI10.1137/16M1093380zbMath1378.35044arXiv1609.02866OpenAlexW2963709756MaRDI QIDQ4596067

Jacob Bedrossian, Siming He

Publication date: 8 December 2017

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.02866

zbMATH Keywords

periodic boundary conditionsenhanced dissipationcritical masshypocoercivityparabolic-elliptic systemPatlak-Keller-Segel equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) A priori estimates in context of PDEs (35B45) Cell movement (chemotaxis, etc.) (92C17) Blow-up in context of PDEs (35B44) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items (23)

Diffusion and mixing in fluid flow via the resolvent estimate ⋮ Suppression of blow-up in parabolic–parabolic Patlak–Keller–Segel via strictly monotone shear flows ⋮ ERRATUM: Suppression of Blow-Up in Patlak--Keller--Segel Via Shear Flows ⋮ Suppression of blow-up in Patlak-Keller-Segel-Navier-Stokes system via the Couette flow ⋮ Mixing for Generic Rough Shear Flows ⋮ Enhanced dissipation and Taylor dispersion in higher‐dimensional parallel shear flows ⋮ Global regularity and stability analysis of the Patlak-Keller-Segel system with flow advection in a bounded domain: a semigroup approach ⋮ Enhanced dissipation by circularly symmetric and parallel pipe flows ⋮ Global well-posedness for aggregation equation with time-space nonlocal operator and shear flow ⋮ Enhanced Dissipation and Blow-Up Suppression in a Chemotaxis-Fluid System ⋮ Global solutions of aggregation equations and other flows with random diffusion ⋮ Bound/positivity preserving SAV schemes for the Patlak-Keller-Segel-Navier-Stokes system ⋮ Hydrodynamic stability at high Reynolds number ⋮ Existence of weak solutions for porous medium equation with a divergence type of drift term ⋮ Suppressing chemotactic blow-up through a fast splitting scenario on the plane ⋮ Boundedness in a chemotaxis-fluid system involving a saturated sensitivity and indirect signal production mechanism ⋮ Phase separation in the advective Cahn-Hilliard equation ⋮ Suppression of blow up by a logistic source in 2D Keller-Segel system with fractional dissipation ⋮ Global existence for the two-dimensional Kuramoto-Sivashinsky equation with a shear flow ⋮ Dissipation enhancement of planar helical flows and applications to three-dimensional Kuramoto-Sivashinsky and Keller-Segel equations ⋮ Suppression of epitaxial thin film growth by mixing ⋮ Convection-induced singularity suppression in the Keller-Segel and other non-linear PDEs ⋮ Delayed blow-up by transport noise

Cites Work

• Unnamed Item
• Unnamed Item
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• Invariant measures for passive scalars in the small noise inviscid limit
• Suppression of chemotactic explosion by mixing
• On the stability threshold for the 3D Couette flow in Sobolev regularity
• Enhanced dissipation, hypoellipticity, and anomalous small noise inviscid limits in shear flows
• Some controllability results for the 2D Kolmogorov equation
• Functional inequalities, thick tails and asymptotics for the critical mass Patlak-Keller-Segel model
• Model for chemotaxis
• Global solutions of some chemotaxis and angiogenesis system in high space dimension
• Volume effects in the Keller--Segel model: energy estimates preventing blow-up
• Short and long time behavior of the Fokker-Planck equation in a confining potential and applications
• A user's guide to PDE models for chemotaxis
• Nonlinear aspects of chemotaxis
• Competing symmetries, the logarithmic HLS inequality and Onofri's inequality on \(S^ n\)
• From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I
• Weak solutions to a parabolic-elliptic system of chemotaxis
• The Sobolev stability threshold for 2D shear flows near Couette
• Preventing blow up in a chemotaxis model
• Isotropic hypoelliptic and trend to equilibrium for the Fokker-Planck equation with a high-degree potential
• Null controllability of Kolmogorov-type equations
• Diffusion and mixing in fluid flow
• Averaging and spectral properties for the 2D advection-diffusion equation in the semi-classical limit for vanishing diffusivity
• Singularity patterns in a chemotaxis model
• The logarithmic HLS inequality for systems on compact manifolds
• Transient anomalous diffusion in Poiseuille flow
• Metastability and rapid convergence to quasi-stationary bar states for the two-dimensional Navier–Stokes equations
• Random walk with persistence and external bias
• Strained spiral vortex model for turbulent fine structure
• Infinite time aggregation for the critical Patlak‐Keller‐Segel model in ℝ²
• Diffusion in Fluid Flow: Dissipation Enhancement by Flows in 2D
• Convergence of the Mass-Transport Steepest Descent Scheme for the Subcritical Patlak–Keller–Segel Model
• How rapidly is a passive scalar mixed within closed streamlines?
• On Explosions of Solutions to a System of Partial Differential Equations Modelling Chemotaxis
• Differential Topology
• The Cauchy problem and self-similar solutions for a nonlinear parabolic equation
• Rapid relaxation of an axisymmetric vortex
• Hypocoercivity for linear kinetic equations conserving mass
• Spectral Asymptotics for Large Skew-Symmetric Perturbations of the Harmonic Oscillator
• The 8π‐problem for radially symmetric solutions of a chemotaxis model in the plane
• The measure of the critical values of differentiable maps
• Enhanced dissipation and inviscid damping in the inviscid limit of the Navier-Stokes equations near the two dimensional Couette flow

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