### Asymptotic stability of mild solutions to the Navier-Stokes equations

##### CAMS Colloquium
• Date:
Monday, April 8, 2013
• Time:
3:30 PM to 4:30 PM
• Campus:
University Park Campus
• Venue:
Kaprelian Hall (KAP)
• Room:
414

Description:

Maria Schonbek, UC Santa Cruz

Abstract: We consider the initial value problem for the Navier-Stokes equations modeling an incompressible fluid in three dimensions:

u_t + u \cdot \nabla u + \nabla p = \Delta u + F,   (x, t) \in \Bbb{R}^3 \times (0, \infty),
div u = 0,
u(x, 0) = u_0(x).

It is well-known that this problem has a unique global-in-time mild solution for a sufficiently small initial conditin u_0 and for a small external force F in suitable scaling invariant spaces.  We show that these global-in-time mild solutions are asymptotically stable under every (arbitrary large) L^2-perturbation of their initial conditions.

The work is joint with Grsegorz Karch and Dominika Pilarczyk.
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