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Main Authors:	Li, Zhen, Shen, Shunlin, Zhang, Zhifei
Format:	Preprint
Published:	2026
Subjects:	Analysis of PDEs
Online Access:	https://arxiv.org/abs/2603.01797
Tags:	Add Tag No Tags, Be the first to tag this record!

Stability threshold of close-to-Couette shear flows with no-slip boundary conditions in 2D
by: Bedrossian, Jacob, et al.
Published: (2025)

Quantitative stability for the 2D Couette flow on the infinite channel with non-slip boundary condition
by: Chen, Qionglei, et al.
Published: (2025)

$l^{2}$-decoupling and the unconditional uniqueness for the Boltzmann equation
by: Chen, Xuwen, et al.
Published: (2025)

Global stability of the inhomogeneous sheared Boltzmann equation in torus
by: Duan, Renjun, et al.
Published: (2025)

On the stability of shear flows in bounded channels, II: non-monotonic shear flows
by: Ionescu, Alexandru D., et al.
Published: (2022)

Sharp $H_{x}^{s}$ Ill-posedness of the Hard-sphere Boltzmann Equation
by: Chen, Xuwen, et al.
Published: (2026)

On the mean-field and semiclassical limit from quantum $N$-body dynamics
by: Chen, Xuwen, et al.
Published: (2023)

Derivation of the compressible Euler equations from the dynamics of interacting Bose gas in the hard-core limit regime
by: Chong, Jacky, et al.
Published: (2024)

Well/Ill-posedness of the Boltzmann Equation with Soft Potential
by: Chen, Xuwen, et al.
Published: (2023)

Global derivation of the 1D Vlasov-Poisson equation from quantum many-body dynamics with screened Coulomb potential
by: Chen, Xuwen, et al.
Published: (2024)

Asymptotic stability of the Kolmogorov flow at high Reynolds numbers
by: Chen, Qi, et al.
Published: (2025)

Structure stability of steady supersonic shear flow with inflow boundary conditions
by: Jiang, Song, et al.
Published: (2025)

Asymptotic stability of shear flows for 2D Euler equations at Yudovich regularity
by: Guo, Dengjun, et al.
Published: (2026)

The derivation of the compressible Euler equation from quantum many-body dynamics
by: Chen, Xuwen, et al.
Published: (2021)

Quantitative stability of the 2D Monotone shear flow for Boussinesq equation in a finite channel
by: Chen, Qionglei, et al.
Published: (2026)

Nonlinear stability of 2-D Couette flow for the compressible Navier-Stokes equations at high Reynolds number
by: Li, Minling, et al.
Published: (2025)

Asymptotic linear stability of columnar vortices driven by Coriolis force
by: Miao, Shuang, et al.
Published: (2026)

Nonlinear stability threshold for 3D compressible Couette flow
by: Li, Rui, et al.
Published: (2026)

Global stability for the compressible isentropic magnetohydrodynamic equations in 3D bounded domains with Navier-slip boundary conditions
by: Liu, Yang, et al.
Published: (2025)

Asymptotic analysis of the Navier-Stokes equations in a thin domain with power law slip boundary conditions
by: Anguiano, María, et al.
Published: (2025)

Critical mass threshold for the 2D Patlak-Keller-Segel-Navier-Stokes system
by: Wang, Wendong, et al.
Published: (2026)

Global stability for compressible isentropic Navier-Stokes equations in 3D bounded domains with Navier-slip boundary conditions
by: Liu, Yang, et al.
Published: (2025)

Stability threshold for 2D shear flows of the Boussinesq system near Couette
by: Bian, Dongfen, et al.
Published: (2020)

Nonlinear stability for 3-D plane Poiseuille flow in a finite channel
by: Chen, Qi, et al.
Published: (2023)

Asymptotic stability of symmetric flows with viscous inflow boundary condition
by: Guo, Yan, et al.
Published: (2026)

The optimal transition threshold for the 2D Couette flow in the infinite channel
by: Chen, Qionglei, et al.
Published: (2025)

Stabilization of nonautonomous Navier-Stokes flows under dynamic slip boundary conditions
by: Priyasad, Buddhika, et al.
Published: (2026)

Infinite Prandtl number convection with Navier-slip boundary conditions
by: Seis, Christian
Published: (2025)

Viscosity driven instability of shear flows without boundaries
by: Li, Hui, et al.
Published: (2024)

Zero-viscosity limit of the chemotaxis-Navier-Stokes equations with the Navier-slip boundary condition
by: Li, Bolun, et al.
Published: (2026)

Improved stability threshold for 2D Navier-Stokes Couette flow in an infinite channel
by: Liang, Tao, et al.
Published: (2025)

Incompressible and vanishing vertical viscosity limit for the compressible Navier-Stokes system with Dirichlet boundary conditions
by: Masmoudi, Nader, et al.
Published: (2025)

Global uniform regularity for the 3D incompressible MHD equations with slip boundary condition near an equilibrium
by: Gao, Jincheng, et al.
Published: (2024)

Well-posedness of the Stokes equations on a wedge with Navier-slip boundary conditions
by: Bravin, Marco, et al.
Published: (2024)

A stochastic fluid-structure interaction problem with the Navier slip boundary condition
by: Tawri, Krutika
Published: (2024)

Nishida-Smoller type large solutions for the compressible Navier-Stokes equations with slip boundary conditions in 3D exterior domains
by: Xie, Minghong, et al.
Published: (2025)

A nonlinear instability result to the Navier-Stokes equations with Navier slip boundary conditions
by: Nguyen, Tien-Tai
Published: (2025)

Transition threshold for the Navier-Stokes-Coriolis system at high Reynolds numbers
by: Li, Minling, et al.
Published: (2025)

Asymptotic behavior of solutions to elliptic problems with Robin boundary conditions
by: Chen, Mengyao, et al.
Published: (2026)

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// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

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