论文标题
关于与真空的2D完全可压缩系统的库奇问题的强大解决方案的存在和爆炸标准
On Existence and Blowup Criterion of Strong Solutions to Cauchy Problem of 2D Full Compressible Navier-Stokes System with Vacuum
论文作者
论文摘要
本文调查了二维完全可压缩的Navier-Stokes系统的库奇问题，其密度和无限时温度消失。对于强溶液，一些先验加权的$ l^2（r^2）$ - 速度梯度的规范是通过$ a_p $ stripts的技术和取消奇异性获得的。基于此关键的加权估计和对速度和温度的一些基本加权分析，我们通过两级近似方案建立了具有初始真空的强溶液的局部存在和独特性。同时，对于（1.8）中的$ q_1 $和$ q_2 $，$ l^\ infty_tl^{q_1} _x $ - 速度的norm和$ l^2_tl^{q_2} _x $ - 最初是最初得出的。此外，我们仅根据与温度无关的速度差异的最大差异标准获得爆炸标准。
This paper investigates the Cauchy problem of two-dimensional full compressible Navier-Stokes system with density and temperature vanishing at infinity. For the strong solutions, some a priori weighted $L^2(R^2)$-norm of the gradient of velocity is obtained by the techniques of $A_p$ weights and cancellation of singularity. Based on this key weighted estimate and some basic weighted analysis of velocity and temperature, we establish the local existence and uniqueness of strong solutions with initial vacuum by means of a two-level approximation scheme. Meanwhile, for $q_1$ and $q_2$ as in (1.8), the $L^\infty_tL^{q_1}_x$-norm of velocity and the $L^2_tL^{q_2}_x$-norm of temperature are derived originally. Moreover, we obtain a blowup criterion only in terms of the temporal integral of the maximum norm of divergence of velocity, which is independent of the temperature.
