  The pressure-temperature phase diagram of the orthorhombic ferromagnetic
superconductor UCoGe was determined by resistivity measurements up to
$10.5~$GPa. The Curie temperature $T_C$ is suppressed with pressure and
vanishes at the critical pressure $p_c\approx1~$GPa. Superconductivity is
observed in both the ferromagnetic state at low pressure, and in the
paramagnetic state above $p_c$ up to about 4$~$GPa. Non-Fermi liquid behavior
appears in a large pressure range. The resistivity varies linearly with
temperature around $p_c$ and evolves continuously with pressure to a $T^2$
Fermi-liquid behavior for $p \gtrapprox 5$~GPa. The residual resistivity as a
function of pressure shows a maximum far above $p_c$ at $p^\star=7.2~$GPa and
the amplitude of the inelastic scattering term of the resistivity decreases by
more than one order in magnitude at $p^\star$, which appears to mark the
entrance into a weakly correlated regime. The pressure dependence of the upper
critical field for magnetic field applied along the $b$ and $c$ axis
illustrates the drastic difference in the field dependence of the ferromagnetic
superconducting pairing. While for $H\parallel b$ axis $H_{c2}(T)$ is driven by
the suppression of the ferromagnetic order, it is dominated by the strong
initial suppression of the ferromagnetic fluctuations for a field applied in
the easy magnetization axis $c$.
