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On two-dimensional Navier-Stokes flows with rotational symmetries. (English) Zbl 1179.35215
The authors study the decay (both time and space) of solutions of the incompressible Navier-Stokes equations in \(\mathbb{R}^2\) based on decay conditions on the initial data. A general order of decay of the solution is given. Higher order decay is shown to be possible if the initial data satisfies not only a faster decay but additionally a rotational symmetry, expressed in terms of covariance of the initial data with respect to a dihedral group.

MSC:
35Q30 Navier-Stokes equations
76E07 Rotation in hydrodynamic stability
76D05 Navier-Stokes equations for incompressible viscous fluids
35B40 Asymptotic behavior of solutions to PDEs
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