We present new measurements of the abundance of galaxies with a given circular velocity in the Local Volume : a region centered on the Milky Way Galaxy and extending to distance \sim 10 Mpc .
The sample of \sim 750 mostly dwarf galaxies provides a unique opportunity to study the abundance and properties of galaxies down to absolute magnitudes M _ { B } \approx - 10 , and virial masses M _ { vir } = 10 ^ { 9 } \mbox { $M _ { \odot } $ } .
We find that the standard \Lambda CDM model gives remarkably accurate estimates for the velocity function of galaxies with circular velocities V \gtrsim 70 \mbox { km~ { } s$ { } ^ { -1 } $ } and corresponding virial masses M _ { vir } \gtrsim 5 \times 10 ^ { 10 } \mbox { $M _ { \odot } $ } , but it badly fails by over-predicting \sim 5 times the abundance of large dwarfs with velocities V = 30 - 40 \mbox { km~ { } s$ { } ^ { -1 } $ } .
The Warm Dark Matter ( WDM ) models can not explain the data either , regardless of mass of WDM particle .
Just as in previous observational studies , we find a shallow asymptotic slope dN / d \log V \propto V ^ { \alpha } , \alpha \approx - 1 of the velocity function , which is inconsistent with the standard \Lambda CDM model that predicts the slope \alpha = -3 .
Though reminiscent to the known overabundance of satellites problem , the overabundance of field galaxies is a much more difficult problem .
For the standard \Lambda CDM model to survive , in the 10 Mpc radius of the Milky Way there should be 1000 not yet detected galaxies with virial mass M _ { vir } \approx 10 ^ { 10 } \mbox { $M _ { \odot } $ } , extremely low surface brightness and no detectable HI gas .
So far none of this type of galaxies have been discovered .