| Contents |
| We consider the uniqueness of bounded continuous $L^{3}_w$-solutions on the whole time axis to the Navier-Stokes equations in $3$-dimensional unbounded domains. Thus far,
uniqueness of such solutions to the Navier-Stokes equations in unbounded domain,
roughly speaking, is known only for a small solution in $BC(R;L^{3}_w)$ within the class of solutions which have sufficiently small $L^{\infty}( L^{3}_w)$-norm.
In this talk, we discuss another type of uniqueness theorem for solutions in $BC(R;L^{3}_w)$ using a smallness condition for one solution and a precompact range condition for the other one. |
|