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Ladyzhenskaya is famous for fluid dynamics and partial differential equations, both of which are beyond my pay grade. And she worked on the Navier-Stokes equations. Does this circle with the arrows represent anything in particular?

All I know from differential equations is that they sometimes involve arrows in "direction fields", which may be a connection.

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The equation in the picture is the Navier–Stokes momentum equation in convective form. The part inside the O looks like a cross-section of (the velocity field of) a flow between two rotating cylinders, mentioned in Ladyzhenskaya's Mathematical Analysis of Navier-Stokes Equations for Incompressible Liquids, 6.4, among other places, the so-called Taylor-Couette flow (spiral vortex). But this is not something Ladyzhenskaya worked on specifically.

It is also similar to a picture of (the direction field of) an unstable spiral surrounded by a limit cycle. Those appear in some finite-dimensional reductions of the Navier-Stokes equations (see e.g. Wang Five-Mode System of the Navier-Stokes Equations on a Torus), but this is even further from what she worked on. So it could just be a cute picture of a "fluid flow" that fits nicely into letter O.

Ladyzhenskaya Google Doodle

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