论文标题
部分可观测时空混沌系统的无模型预测
Global existence versus blow-up for multi-d hyperbolized compressible Navier-Stokes equations
论文作者
论文摘要
我们认为在两个或三个空间尺寸中的非异形可压缩的Navier-Stokes方程式，其中傅立叶定律的热传导被Cattaneo定律所取代，而经典的牛顿流则被修订后的麦克斯韦流动所取代。我们表明，这种新模型存在物理熵。在两种特殊情况下，我们显示了解决方案的全球良好性，具有较小的初始数据，并在有限的时间内用于一类大型初始数据的解决方案。此外，对于消失的松弛参数，证明解决方案（如果存在）会收敛到经典系统的解决方案。
We consider the non-isentropic compressible Navier-Stokes equations in two or three space dimensions for which the heat conduction of Fourier's law is replaced by Cattaneo's law and the classical Newtonian flow is replaced by a revised Maxwell flow. We show that a physical entropy exists for this new model. For two special cases, we show the global well-posedness of solutions with small initial data and the blow-up of solutions in finite time for a class of large initial data. Moreover, for vanishing relaxation parameters, the solutions (if it exists) are shown to converge to solutions of the classical system.
