| Abstract: |
| We consider the two-dimensional Cauchy problem of the full compressible Navier-Stokes equations with far-field vacuum in $\mathbb{R}^2$, where the viscosity and heat-conductivity coefficients depend on the absolute temperature $\theta$ in the form of $\theta^\nu$ with $\nu>0$. Due to the appearance of the vacuum, the momentum equation are both degenerate in the time evolution and spatial dissipation, which makes the study on the well-posedness challenging. By establishing some new singular-weighted (negative powers of the density $\rho$) estimates of the solution, we establish the local-in-time well-posedness of the regular solution with far-field vacuum in terms of $\rho$, the velocity $u$ and the entropy $S$. Moreover, the uniform regularity of the entropy $S$ in $\mathbb{R}^2$ is established, i.e., $S-\bar{S}\in C([0,T];H^3(\mathbb{R}^2))$ for some constant $\bar{S}$. |
|