A quantitative stability theorem for the stably stratified Couette shear flow of the two-dimensional fully dissipative Boussinesq system posed on the unbounded plane R^2, in the large-Richardson-number regime R > 1/4 with comparable viscosity and density diffusivity. For perturbations of controlled size in a low-order anisotropic Sobolev space it establishes nonlinear asymptotic stability together with explicit decay rates for three distinct mechanisms: enhanced dissipation (shear accelerates viscous decay of non-zero horizontal modes), Taylor dispersion (shear-enhanced diffusion of the density), and inviscid damping (decay of the velocity and density driven by mixing rather than viscosity). It is the first such result on the fully unbounded domain, and it also transfers the corresponding linear estimates from the channel T x R to R^2.
Proves quantitative nonlinear asymptotic stability of the stably stratified Couette shear flow for the 2D fully dissipative Boussinesq system on the whole plane R^2, in the large-Richardson-number re…