The nonlinear stability threshold for 3D compressible Couette flow is O(ν^{3/2}).
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Finite-time vorticity blow-up is shown to exist for the forced 2D non-homogeneous Euler equations via adaptation of a prior Boussinesq construction.
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Nonlinear stability threshold for 3D compressible Couette flow
The nonlinear stability threshold for 3D compressible Couette flow is O(ν^{3/2}).
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Vorticity blow-up for the 2D incompressible non-homogeneous Euler equations with uniform $C^{1,\sqrt{\frac{4}{3}}-1-\varepsilon}$ force
Finite-time vorticity blow-up is shown to exist for the forced 2D non-homogeneous Euler equations via adaptation of a prior Boussinesq construction.