5 citations · 10 across the 7 of their papers we have counts for
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On stability estimates for the inviscid Boussinesq equations
Christian Zillinger
We consider the (in)stability problem of the inviscid 2D Boussinesq equations near a combination of a shear flow and a stratified temperature with .…
On variable viscosity and enhanced dissipation
Xian Liao, Christian Zillinger
In this article we consider the 2D Navier-Stokes equations with variable viscosity depending on the vertical position. As our main result we establish linear enhanced dissipation n…
On echo chains in the linearized Boussinesq equations around traveling waves
Christian Zillinger
We consider the 2D Boussinesq equations with viscous but without thermal dissipation and observe that in any neighborhood of Couette flow and hydrostatic balance (with respect to l…
On Enhanced Dissipation for the Boussinesq Equations
Christian Zillinger
In this article we consider the stability and damping problem for the 2D Boussinesq equations with partial dissipation near a two parameter family of stationary solutions which inc…
On Echo Chains in Landau damping: Self-similar Solutions and Gevrey 3 as a Linear Stability Threshold
Christian Zillinger
We show that the linearized Vlasov-Poisson equations around self-similar non-homogeneous states near zero contain the full plasma echo mechanism, yielding Gevrey 3 as a critical st…
On the Smallness Condition in Linear Inviscid Damping: Monotonicity and Resonance Chains
Yu Deng, Christian Zillinger
We consider the linearized Euler equations around a smooth, bilipschitz shear profile on . We construct an explicit flow which exhibits linea…