  We study $AdS_3$ supersymmetric vacua in N=4 and N=8, three dimensional
gauged supergravities, with scalar manifolds $(\frac{SO(4,4)}{SO(4)\times
SO(4)})^2$ and $\frac{SO(8,8)}{SO(8)\times SO(8)}$, non-semisimple Chern-Simons
gaugings $SO(4)\ltimes {\bf R}^6$ and $(SO(4)\ltimes {\bf R}^6)^2$,
respectively. These are in turn equivalent to SO(4) and $SO(4)\times SO(4)$
Yang-Mills theories coupled to supergravity. For the N=4 case, we study
renormalization group flows between UV and IR $AdS_3$ vacua with the same
amount of supersymmetry: in one case, with (3,1) supersymmetry, we can find an
analytic solution whereas in another, with (2,0) supersymmetry, we give a
numerical solution. In both cases, the flows turn out to be v.e.v. flows, i.e.
they are driven by the expectation value of a relevant operator in the dual
$SCFT_2$. These provide examples of v.e.v. flows between two $AdS_3$ vacua
within a gauged supergravity framework.
