For the 3D Boussinesq system near Couette flow with constant background temperature, H2 perturbations satisfying velocity and temperature smallness bounds of order ν and ν² respectively stay global in time.
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Stability threshold of Couette flow for 3D Boussinesq system in Sobolev spaces
For the 3D Boussinesq system near Couette flow with constant background temperature, H2 perturbations satisfying velocity and temperature smallness bounds of order ν and ν² respectively stay global in time.