Siming He

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20242026

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math.AP2024

Transition Threshold for Strictly Monotone Shear Flows in Sobolev Spaces

Rajendra Beekie, Siming He

We study the stability of spectrally stable, strictly monotone, smooth shear flows in the 2D Navier-Stokes equations on $T \times R$ with small viscosity $I^½$ . We…

math.AP2024

Uniform Inviscid Damping and Inviscid Limit of the 2D Navier-Stokes equation with Navier Boundary Conditions

Jacob Bedrossian, Siming He, Sameer Iyer +1

We consider the 2D, incompressible Navier-Stokes equations near the Couette flow, $I ¨ ^{(N S)} = 1 + I^µ I ¨ $ , set on the channel $T \times [- 1, 1]$ , supplemented with Navier b…

math.AP2024

Pseudo-Gevrey Smoothing for the Passive Scalar Equations near Couette

Jacob Bedrossian, Siming He, Sameer Iyer +1

In this article, we study the regularity theory for two linear equations that are important in fluid dynamics: the passive scalar equation for (time-varying) shear flows close to C…