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1. Bifurcation and inviscid limit


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      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?


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          Problem 1.2.

          [Bartosz Protas] Study the bifurcation problem of Taylor–Couette instability.


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              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 $\delta _{\{z = z _i\}}$.


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                  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.