论文标题
经典解决方案的全球存在和最佳衰减速率，用于3-D辐射流体动力学，没有热电导率
Global existence and optimal decay rate of the classical solution to 3-D Radiative Hydrodynamics with and without Heat Conductivity
论文作者
论文摘要
在两个不同的条件下，有和没有热电导率，研究了3-D辐射流体动力学模型的经典解。在这两种情况下，我们都证明了以下结果。首先，当固定状态周围的初始扰动的$ h^k $规范足够小，并且整数$ k \ geq2 $时，证明存在这种库奇问题的独特经典解决方案。其次，如果我们进一步假设初始扰动的$ l^1 $规范也很小，则解决方案的I级（$ 0 \ leq i \ leq k-2 $）的衍生物具有$（1+t）^{ - \ frac 34- \ frac 34- \ frac i2} $的衰减率。第三，从上面的结果中我们可以看到，对于辐射流体动力学，辐射可以与热传导相同的工作，这意味着，如果导热系数系数变为$ 0 $，则由于辐射的效果，系统的溶解度和溶液的衰减速率保持相同。
The classical solution of the 3-D radiative hydrodynamics model is studied in $H^k$-norm under two different conditions, with and without heat conductivity. We have proved the following results in both cases. First, when the $H^k$ norm of the initial perturbation around a constant state is sufficiently small and the integer $k\geq2$, a unique classical solution to such Cauchy problem is shown to exist. Second, if we further assume that the $L^1$ norm of the initial perturbation is small too, the i-order($0\leq i\leq k-2$) derivative of the solutions have the decay rate of $(1+t)^{-\frac 34-\frac i2}$ in $H^2$ norm. Third, from the results above we can see that for radiative hydrodynamics, the radiation can do the same job as the heat conduction, which means if the thermal conductivity coefficient turns to $0$, because of the effect of radiation, the solvability of the system and decay rate of the solution stay the same.
