Time-dependent flows and their applications in parabolic-parabolic Patlak-Keller-Segel systems. I: Alternating flows

Partial differential equations of mathematical physics and other areas of application (35Qxx) Parabolic equations and parabolic systems (35Kxx) Qualitative properties of solutions to partial differential equations (35Bxx)

Cites Work

Uniqueness and long time asymptotic for the Keller-Segel equation: the parabolic-elliptic case
Suppression of chemotactic explosion by mixing
A coupled Keller-Segel-Stokes model: global existence for small initial data and blow-up delay
On the stability threshold for the 3D Couette flow in Sobolev regularity
Enhanced dissipation, hypoellipticity, and anomalous small noise inviscid limits in shear flows
A coupled chemotaxis-fluid model: global existence
On Landau damping
Chemotaxis-fluid coupled model for swimming bacteria with nonlinear diffusion: global existence and asymptotic behavior
Transition threshold for the 2-D Couette flow in a finite channel
Model for chemotaxis
Volume effects in the Keller--Segel model: energy estimates preventing blow-up
The parabolic-parabolic Keller-Segel model in \(\mathbb R^2\)
Critical mass for a Patlak-Keller-Segel model with degenerate diffusion in higher dimensions
The Sobolev stability threshold for 2D shear flows near Couette
Suppression of plasma echoes and Landau damping in Sobolev spaces by weak collisions in a Vlasov-Fokker-Planck equation
Global well-posedness and blow-up for the 2-D Patlak-Keller-Segel equation
Suppressing chemotactic blow-up through a fast splitting scenario on the plane
Locally bounded global solutions in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion
Existence of smooth solutions to coupled chemotaxis-fluid equations
Phase separation in the advective Cahn-Hilliard equation
Vortex stretching and enhanced dissipation for the incompressible 3D Navier-Stokes equations
Enhanced dissipation, hypoellipticity for passive scalar equations with fractional dissipation
Global existence for the two-dimensional Kuramoto-Sivashinsky equation with a shear flow
Enhanced dissipation and Hörmander's hypoellipticity
Global hypocoercivity of kinetic Fokker-Planck-alignment equations
Inviscid damping and enhanced dissipation of the boundary layer for 2D Navier-Stokes linearized around Couette flow in a channel
Separation of time-scales in drift-diffusion equations on \(\mathbb{R}^2\)
Existence, uniqueness and asymptotic behavior of the solutions to the fully parabolic Keller-Segel system in the plane
Time global existence and finite time blow-up criterion for solutions to the Keller-Segel system coupled with the Navier-Stokes fluid
Linear inviscid damping and enhanced dissipation for the Kolmogorov flow
On pseudospectral bound for non-selfadjoint operators and its application to stability of Kolmogorov flows
Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system
Diffusion and mixing in fluid flow
Quenching of combustion by shear flows
Hypoelliptic second order differential equations
Suppression of blow-up in Patlak-Keller-Segel-Navier-Stokes system via the Couette flow
Stability threshold of two-dimensional Couette flow in Sobolev spaces
Bacterial swimming and oxygen transport near contact lines
Random walk with persistence and external bias
Uniqueness and long time asymptotics for the parabolic–parabolic Keller–Segel equation
Local and global well-posedness for aggregation equations and Patlak–Keller–Segel models with degenerate diffusion
Suppression of blow-up in parabolic–parabolic Patlak–Keller–Segel via strictly monotone shear flows
Dynamics Near the Subcritical Transition of the 3D Couette Flow I: Below Threshold Case
Infinite time aggregation for the critical Patlak‐Keller‐Segel model in ℝ²
COUPLED CHEMOTAXIS FLUID MODEL
Hypocoercivity
On Explosions of Solutions to a System of Partial Differential Equations Modelling Chemotaxis
Minimal Mass Blowup Solutions for the Patlak‐Keller‐Segel Equation
ERRATUM: Suppression of Blow-Up in Patlak--Keller--Segel Via Shear Flows
Dissipation enhancement by mixing
Quenching of flames by fluid advection
The Cauchy problem and self-similar solutions for a nonlinear parabolic equation
Global Solutions to the Coupled Chemotaxis-Fluid Equations
Convection-induced singularity suppression in the Keller-Segel and other non-linear PDEs
Quasi-streamwise vortices and enhanced dissipation for incompressible 3D Navier–Stokes equations
Refined Description and Stability for Singular Solutions of the 2D Keller‐Segel System
Stirring speeds up chemical reaction
Pseudospectral Bound and Transition Threshold for the 3D Kolmogorov Flow
On the Relation between Enhanced Dissipation Timescales and Mixing Rates
Global Large-Data Solutions in a Chemotaxis-(Navier–)Stokes System Modeling Cellular Swimming in Fluid Drops
Enhanced dissipation for the 2D couette flow in critical space
Enhanced dissipation and inviscid damping in the inviscid limit of the Navier-Stokes equations near the two dimensional Couette flow
Orientation mixing in active suspensions
Exponential mixing for random dynamical systems and an example of Pierrehumbert
Anomalous dissipation for the forced 3D Navier-Stokes equations
Taylor dispersion and phase mixing in the non-cutoff Boltzmann equation on the whole space
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