On strong convergence to 3D steady vortex sheets |
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Authors: | Quansen Jiu Zhouping Xin |
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Institution: | a School of Mathematical Sciences, Capital Normal University, Beijing 100037, PR China b IMS and Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong c Center for Nonlinear Studies, Northwest University, Xian, China |
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Abstract: | In this paper, we first establish a strong convergence criterion of approximate solutions for the 3D steady incompressible Euler equations. For axisymmetric flows, under the assumption that the vorticity is of one sign and uniformly bounded in L1 space, we obtain a sufficient and necessary condition for the strong convergence in of approximate solutions. Furthermore, for one-sign and L1-bounded vorticity, it is shown that if a sequence of approximate solutions concentrates at an isolated point in (r,z)-plane, then the concentration point can appear neither in the region near the axis (including the symmetry axis itself) nor in the region far away from the axis. Finally, we present an example of approximates solutions which converge strongly in by using Hill's spherical vortex. |
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Keywords: | 35Q35 76B03 |
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