论文标题
全球旋转运动旋转运动的解决方案，用圆柱形对称性
Global solutions to rotating motion of isentropic flows with cylindrical symmetry
论文作者
论文摘要
我们关注的是具有圆柱对称旋转结构的等屈力压缩欧拉方程的全局弱解，其中包括了原点。由于原点上存在奇异性，因此仅考虑了原点$ | \ vec {x} | \ geq1 $的情况，而Chen-glimm \ cite {chen3}已经考虑了。通过使用$ l^{\ infty} $补偿的紧凑型框架和消失的粘度方法证明了近似解决方案的收敛性和一致性。我们观察到，如果爆炸波最初向外移动，以及在原点附近的一定代数速率下以某些代数速率向零移动，则在任何正时速度相同的速率，密度和速度衰减。特别是，假定最初的正常速度是非负的，并且对初始角速度的迹象没有限制。
We are concerned with global weak solutions to the isentropic compressible Euler equations with cylindrically symmetric rotating structure, in which the origin is included. Due to the presence of the singularity at the origin, only the case excluding the origin $|\vec{x}|\geq1$ has been considered by Chen-Glimm \cite{Chen3}. The convergence and consistency of the approximate solutions are proved by using $L^{\infty}$ compensated compactness framework and vanishing viscosity method. We observe that if the blast wave initially moves outwards and if initial density and velocity decay to zero at certain algebraic rate near the origin, then the density and velocity decay at the same rate for any positive time. In particular, the initial normal velocity is assumed to be non-negative, and there is no restriction on the sign of initial angular velocity.
