In this paper, we are first concerned with viscous approximations for the three-dimensional axisymmetric incompressible Euler equations. It is proved that the viscous approximations, which are the solutions of the cor...In this paper, we are first concerned with viscous approximations for the three-dimensional axisymmetric incompressible Euler equations. It is proved that the viscous approximations, which are the solutions of the corresponding Navier-Stokes equations, converge strongly in provided that they have strong convergence in the region away from the symmetry axis. This result has been proved by the authors for the approximate solutions generated by smoothing the initial data, with no restriction of the sign of the initial data. Then we discuss the decay rate for maximal vorticity function, which is established for both approximate solutions generated by smoothing the initial data and viscous approximations respectively. One sufficient condition to guarantee the strong convergence in the region away from the symmetry axis is given, and a decay rate for maximal vorticity function in the region away from the symmetry axis is obtained for non-negative initial vorticity.展开更多
基金partially supported by National Natural Sciences Foundation of China (No.10101014)Beijing Natural Sciences Foundation+1 种基金the Key Project of NSFB-FBEC,by Grants from RGC of HKSAR CUHK4279/00P and CUHK4129/99Pthe generous hospitality and financial support of IMS of The Chinese University of Hong Kongpartially supported by Zheng Ge Ru Funds, Grants from RGC of HKSAR CUHK4279/00P and CUHK4129/99P
文摘In this paper, we are first concerned with viscous approximations for the three-dimensional axisymmetric incompressible Euler equations. It is proved that the viscous approximations, which are the solutions of the corresponding Navier-Stokes equations, converge strongly in provided that they have strong convergence in the region away from the symmetry axis. This result has been proved by the authors for the approximate solutions generated by smoothing the initial data, with no restriction of the sign of the initial data. Then we discuss the decay rate for maximal vorticity function, which is established for both approximate solutions generated by smoothing the initial data and viscous approximations respectively. One sufficient condition to guarantee the strong convergence in the region away from the symmetry axis is given, and a decay rate for maximal vorticity function in the region away from the symmetry axis is obtained for non-negative initial vorticity.
