On the inviscid limit for a fluid with a concentrated vorticity

Communications in Mathematical Physics

Volumn 196, Issue 1, 1998, Pages 53-65

  Marchioro, Carlo ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032474982     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050413     Document Type: Article

References (24)

1. Asano, K.: Zero-viscosity limit of the incompressible Navier-Stokes equations. Preprint 1 and 2 (1988)
2. Beale, J .T., Majda. A.: Rates of convergence for viscous splitting of the Navier-Stokes equations. Math. Comp. 37, 243-259 (1981)
3. Caflisch, R.E., Sammartino, M.: Navier-Stokes equations on an exterior circular domain: Construction of the solution and zero viscosity limit. Preprint (1996)
4. Chemin J.-Y.: A remark on the inviscid limit for twp-dimensional incompressible fluids. Commun. Part. Diff. Eq. 21, 1771-1779 (1996)
5. Constantin, P., Wu, J.: Inviscid limit for vortex patches. Nonlinearity 8, 735-742 (1995)
6. Constantin, P., Wu J.: The Inviscid Limit for Non-Smooth Vorticity. Indiana U. Math. J. 45, 67-81 (1996)
7. Helmholtz, H.: On the integrals of the hydrodynamical equations which express vortex motion. Phil. Mag. 33, 485 (1867)
8. 3. J. Funct. Anal. 9, 296-305 (1972)
9. Kelvin, J.: Mathematical and Physical Papers. Cambridge, Cambridge University Press, 1910
10. Kirchhoff, G.: Vorlesungen über Math. Phys. Leipzig: Teubner, 1876
11. Marchioro, C., Pulvirenti, M.: Euler evolution for singular data and vortex theory. Commun. Math. Phys. 91, 563 (1983)
12. Marchioro, C., Pulvirenti, M.: Vortex methods in two-dimensional fluid mechanics. Lecture Notes in Physics, Vol. 203, Berlin-Heidelberg-New York: Springer-Verlag, 1984
13. Marchioro, C., Pagani, E.: Evolution of Two Concentrated Vortices in a Two-Dimensional Bounded Domain. Math. Meth. Appl. Sci. 8, 328 (1986)
14. Marchioro, C., Pulvirenti, M.: Vortices and Localization in Euler Flows. Commun. Math. Phys. 154, 49 (1993)
15. Marchioro, C., Pulvirenti, M.: Mathematical Theory of Incompressible Non-Viscous Fluids. Applied Mathematical Sciences 96, Berlin-Heidelberg-New York: Springer-Verlag, 1994
16. Marchioro, C.: Euler Evolution for Singular Initial Data and Vortex Theory: A Global Solution. Commun. Math. Phys. 116, 45-55 (1988)
17. Marchioro, C.: On The Vanishing Viscosity Limit for Two-dimensional Navier-Stokes Equation with Singular Initial Data. Math. Meth. Appl. Sci. 12, 463-70 (1990)
18. Marchioro, C.: Bounds on the Growth of the Support of a Vortex Patch. Commun. Math. Phys. 164, 507-524 (1994)
19. Marchioro, C.: On the localization of the vortices. Preprint (1996)
20. Mc.Grath, F: Nonstationary plane flow of viscous and ideal fluids. Arch. Rat. Mech. Anal. 27, 329-348 (1968)
21. Poincaré, H.: Théories des Tourbillons. Paris: George Carré, 1893
22. Sammartino, M., Caflish, R.E.: Zero Viscosity Limit for Analytic Solutions of the Navier-Stokes Equation on a Half-Space I. Existence for Euler and Prandtl Equations. Preprint (1996)
23. Sammartino, M., Caflish, R.E.: Zero Viscosity Limit for Analytic Solutions of the Navier-Stokes Equation on a Half-Space II. Construction of the Navier-Stokes Solution. Preprint (1996)
24. Turkington, B.: On the evolution of a concentrated vortex in an ideal fluid. Arch. Rat. Mech. An. 97, 75 (1987)