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\textbf{SPEAKER}:
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%\textbf{SPEAKER}:
 Christophe Prange, CY Cergy Paris  Universit\'e
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{\bf TITLE}:
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Quantitative regularity for the steady and unsteady 3D Navier-Stokes equations
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{\bf ABSTRACT:}\\
In this talk, I will focus on two aspects of the quantitative regularity theory of solutions to the 3D Navier-Stokes equations. 
First, I will address the local regularity for the steady Navier-Stokes equations near very rough (bumpy, possibly fractal) boundaries. There the emphasis is on large-scale regularity and on local wall laws. 
In the second part of the talk, I will concentrate on the quantitative regularity for the time-dependent Navier-Stokes equations, away from boundaries. There the emphasis is on explicit quantitative control of subcritical norms in terms of scale-invariant quantities. This talk is based on joint works with Mitsuo Higaki and Jinping Zhuge on the one hand, and Tobias Barker on the other hand.




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