Transport coefficients in a two-dimensional Fermi liquid

We calculate variationally the coefficients of thermal conductivity $K_s$, spin diffusion $D_s$, and transverse viscosity ${\eta }_s$ in a two-dimensional Fermi liquid by using the Landau Fermi-liquid theory. The leading temperature dependence at small $T$ is $K_s^{{}^{-1\mathrm{}}}\propto T\ln T$, $D_s^{-1\mathrm{}}\propto T^2\ln T$, and ${\eta }_s^{-1\mathrm{}}\propto T^2$, in contrast with the behavior of a three-dimensional Fermi liquid, $K^{-1\mathrm{}}\propto T$, $D^{-1\mathrm{}}\propto T^2$, and ${\eta }^{-1\mathrm{}}\propto T^2$. The resulting formulas are used to predict $K_s$, $D_s$, and ${\eta }_s$ for the liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ monolayer or partial monolayer which can form on a free surface of superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$.