Acta mathematica scientia,Series B ›› 2018, Vol. 38 ›› Issue (3): 1057-1104.doi: 10.1016/S0252-9602(18)30801-4
• Articles • Previous Articles
Weifeng JIANG1, Kaitai LI2
Received:
2016-02-03
Revised:
2018-03-21
Online:
2018-06-25
Published:
2018-06-25
Contact:
Weifeng JIANG
E-mail:weifengjiang@163.com
Supported by:
This work was supported by NSFC (91330116), State Major Basic Research and Development Project (2011CB 706505), NSFC (11371289), NSFC (11371288).
Weifeng JIANG, Kaitai LI. HELICAL SYMMETRIC SOLUTION OF 3D NAVIER-STOKES EQUATIONS ARISING FROM GEOMETRIC SHAPE OF THE BOUNDARY[J].Acta mathematica scientia,Series B, 2018, 38(3): 1057-1104.
[1] Agmon S. Lectures on elliptic boundary value problems. Princeton, N J:D Van Nostrand Co, Inc, 1965 [2] Constantin P, Foias C. Navier-Stokes Equations. Chicago:University of Chicago Press, 1988 [3] Ettinger B, Titi E S. Global existence and uniqueness of weak solutions of three-dimensional Euler equations with helical symmetry in the absence of vorticity stretching. SIAM J Math Anal, 2009, 41:269-296 [4] Ghidaglia J M. Régularité des solutions de certains problèmes aux limites linéaires liés aux équations d'Euler (French). Comm Partial Differential Equations, 1984, 9:1265-1298 [5] Heywood J G. Navier-Stokes Equations:On the existence, regularity and decay of solutions. Indiana Univ Math J, 1980, 29:639-681 [6] Hüttl T J, Wagner C, Friedrich R. Navier-Stokes solutions of laminar flows based on orthogonal helical co-ordinates. Int J Numer Meth Fluids, 1999, 29:749-763 [7] Ladyzhenskaya O A. The Mathematical Theory of Viscous Incompressible Flow. 2nd ed. New York:Gordon and Breach, 1969 [8] Li K, Huang A. Tensor Analysis and Its Applications. Science Press, Beijing, China and Alpha Science International Ltd, Oxford, UK, 2015 [9] Lions J L, Magenes E. Non-homogeneous Boundary Value Problems and Applications. Vol I. New York:Springer-Verlag, 1972 [10] Lopes Filho M C, Mazzucato A L, Niu D, Nussenzveig Lopes H J, Titi E S. Planar limits of ThreeDimensional incompressible flows with helical symmetry. J Dyn Diff Equations, 2014, 26:843-869 [11] Mahalov A, Titi E S, Leibovich S. Invariant helical subspaces for the Navier-Stokes equations. Arch Rational Mech Anal, 1990, 112:193-222 [12] Temam R. Navier-Stokes Equations. Theory and Numerical Analysis. 3rd ed. Amsterdam:North Holland Pub Co, 1984 [13] Wang S. On a new 3D model for incompressible Euler and Navier-Stokes equations. Acta Mathematica Scientia, 2010, 30B(6):2089-2102 |
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