Realization of regularity coefficients for flows.

We establish sharp relations between several regularity coefficients for flows generated by non-autonomous differential equations. We verify that these relations are sharp by showing that all possible values of the regularity coefficients satisfying these relations are attained by some linear equation with bounded piecewise-continuous coefficient matrix. In addition, we introduce two new regularity coefficients and we obtain sharp relations between these and other coefficients. [ABSTRACT FROM AUTHOR]