分野別セミナー

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.