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PDE Real Analysis Seminar
Seminar information archive ～04/18｜Next seminar｜Future seminars 04/19～
| Date, time & place | Tuesday 10:30 - 11:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|
2009/11/25
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Hermann Sohr (University Paderborn)
Recent results on weak and strong solutions of the Navier-Stokes equations
Hermann Sohr (University Paderborn)
Recent results on weak and strong solutions of the Navier-Stokes equations
[ Abstract ]
Our purpose is to develop the optimal initial value condition for the existence of a unique local strong solution of the Navier-Stokes equations in a smooth bounded domain.
This condition is not only sufficient
- there are several well-known sufficient conditions in this context
- but also necessary, and yields therefore the largest possible class of such strong solutions.
As an application we obtain several extensions of Serrin's regularity condition. A restricted result also holds for completely general domains. Furthermore we extend the well-known class of Leray-Hopf weak solutions with zero boundary conditions and zero divergence to a larger class with corresponding nonzero conditions.
Our purpose is to develop the optimal initial value condition for the existence of a unique local strong solution of the Navier-Stokes equations in a smooth bounded domain.
This condition is not only sufficient
- there are several well-known sufficient conditions in this context
- but also necessary, and yields therefore the largest possible class of such strong solutions.
As an application we obtain several extensions of Serrin's regularity condition. A restricted result also holds for completely general domains. Furthermore we extend the well-known class of Leray-Hopf weak solutions with zero boundary conditions and zero divergence to a larger class with corresponding nonzero conditions.
