$G^{2}$) and Landau damping (in order to ultimately remove the crossings) are necessary to obtain a flow equation with unique solutions. Using this flow equation, it is possible to extrapolate the equation of state from lattice QCD at $\mu=0$ towards $T=0$.

![The solid curves in both graphs are several characteristics of the full HTL flow equation for $2+1$ quark flavors using parameters from the adjustment of the full HTL QPM to lattice data from [@Kar07] shown in Figure \[fig:fullHTL fit quad\]. The characteristic curve emerging from $T_{c}$ is depicted as bold solid line. All crossings have disappeared (left panel). For a comparison, the right panel shows the characteristics of the eQP flow equation using the parameters of the eQP adjustment to the same lattice QCD data (dashed curves).[]{data-label="fig:HTL characteristics"}](HTLcloseup2.eps "fig:")        ![The solid curves in both graphs are several characteristics of the full HTL flow equation for $2+1$ quark flavors using parameters from the adjustment of the full HTL QPM to lattice data from [@Kar07] shown in Figure \[fig:fullHTL fit quad\]. The characteristic curve emerging from $T_{c}$ is depicted as bold solid line. All crossings have disappeared (left panel). For a comparison, the right panel shows the characteristics of the eQP 