On the smallness of the (possible) singular set in space for 3D Navier-Stokes equations.
Dynamics of complex singularities in 1D nonlinear parabolic PDE's
We establish local-in-time smoothing of a simple model nonlinear parabolic PDE in a scale of weighted Bergman spaces on a strip provided the weights are not too singular. This constitutes a very strong smoothing property since an immediate consequence is that the PDE can "push away" an algebraic-type complex singularity provided that the order of the singularity is small enough.
Algebraic lower bounds for the uniform radius of spatial analyticity for the generalized KdV equation
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