Uniqueness for autonomous planar differential equations and the lagrangian formulation of water flows with vorticity

Journal of Nonlinear Mathematical Physics

Volumn 11, Issue 4, 2004, Pages 549-555

  Wahlén, Erik ^a  

^a LUND UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 10044261928     PISSN: 14029251     EISSN: 17760852     Source Type: Journal    
DOI: 10.2991/jnmp.2004.11.4.10     Document Type: Article

References (15)

1. Agarwal, RP, and Lakshmikantham, V. 1993. Uniqueness and Nonuniqueness Criteria for Ordinary Differential Equations, River Edge, NJ:World Scientific Publ. Co., Inc.
2. Majda, AJ, and Bertozzi, AL. 2002. Vorticity and Incompressible Flow, Cambridge:Cambridge University Press.
3. Chemin, JY. 1998. Perfect Incompressible Fluids, New York:Oxford University Press.
4. Constantin, A. 2001. On the deep water wave motion. J. Phys. A, 34:1405–1417.
5. Constantin, A. 2001. Edge waves along a sloping beach. J. Phys. A, 34:9723–9731.
6. Constantin, A, and Escher, J. 2004. Symmetry of steady periodic surface water waves with vorticity. J. Fluid Mech., 498:171–181.
7. Constantin, A, and Strauss, W. 2002. Exact periodic traveling water waves with vorticity. C. R. Math. Acad. Sci. Paris, 335:797–800.
8. Constantin, A, and Strauss, W. 2004. Exact steady periodic water waves with vorticity. Comm. Pure Appl. Math., 57:481–527.
9. Conti, R, and Sansone, G. 1964. Non-Linear Differential Equations, New York:Pergamon Press.
10. Gerstner, F. 1809. Theorie der Wellen samt einer daraus abgeleiteten Theorie der Deichprofile. Ann. Physik, 2:412–445.
11. Johnson, RS. 1997. A Modern Introduction to the Mathematical Theory of Water Waves, Cambridge University Press.
12. Jonsson, I. 1990. Wave-current interactions, in “The Sea” Edited by:LeMehaute, B., Hanes, D., and Wiley, J., 65–120. New York
13. Lighthill, J. 1978. ‘Waves in Fluids’, Cambridge University Press.
14. Thomas, G, and Klopman, G. 1997. Wave-current interactions in the nearshore region, in “Gravity Waves in Water of Finite Depth”, 215–319. United Kingdom:Southhampton.
15. Yudovich, VI. 1963. Non-stationary flow of an incompressible liquid. Zh. Vychisl. Mat. Nat. Fiz., 3:1032–1066.