$\newcommand{\Cat}{{\rm Cat}}$ $\newcommand{\A}{\mathcal A}$ $\newcommand{\freestar}{ \framebox[7pt]{\star} }$

## 1. Bifurcation and inviscid limit

1. #### Problem 1.1.

[Dallas Albritton and Marc Brachet] Rigorous derivation of a Hopf bifurcation in Reynolds number for 2D incompressible Navier–Stokes flow or Gross–Pitaevskii flow passing a (cylindrical) obstacle. Can it be proven without computer-assistant proof?
• #### Problem 1.2.

[Bartosz Protas] Study the bifurcation problem of Taylor–Couette instability.
• #### Problem 1.3.

[Gautam Iyer] In 2D, formulate the random vortex methods analog to the model of a flow past an obstacle (Stochastic ODE). Is there a stability transition (Hopf bifurcation) in the Reynolds number? \begin{align*} \frac {dz _i}{dt} = \sum _{j \neq i} v (z _j) + u _{\text{background}}. \end{align*} where $v (z _i)$ is the velocity generated by a point vorticy $\delta _{\{z = z _i\}}$.
• #### Problem 1.4.

[Alexis Vasseur] Study the inviscid limit of the non-unique Leray solution to the forced Navier–Stokes equation.

Cite this as: AimPL: Criticality and stochasticity in quasilinear fluid systems, available at http://aimpl.org/stochasticfluid.