Artículos de revistas
Existence Of A Weak Solution In L P To The Vortex-wave System
Registro en:
Journal Of Nonlinear Science. , v. 21, n. 5, p. 685 - 703, 2011.
9388974
10.1007/s00332-011-9097-y
2-s2.0-80053344671
Autor
Lopes Filho M.C.
Miot E.
Nussenzveig Lopes H.J.
Institución
Resumen
The vortex-wave system is a coupling of the two-dimensional vorticity equation with the point-vortex system. It is a model for the motion of a finite number of concentrated vortices moving in a distributed vorticity background. In this article, we prove existence of a weak solution to this system with an initial background vorticity in L p, p>2, up to the time of first collision of point vortices. © 2011 Springer Science+Business Media, LLC. 21 5 685 703 Chemin, J.-Y., Sur le mouvement des particules d'un fluide parfait incompressible bidimensionel (1991) Invent. Math., 103, pp. 599-629. , 1091620 0739.76010 10.1007/BF01239528 Delort, J.-M., Existence de nappes de tourbillon en dimension deux (1991) J. Am. Math. Soc., 4, pp. 553-586. , 1102579 0780.35073 10.1090/S0894-0347-1991-1102579-6 Diestel, J., Uhl, J., (1977) Vector Measures Mathematical Surveys, 15. , AMS Providence 0369.46039 Gamblin, P., Iftimie, D., Sideris, T., On the evolution of compactly supported planar vorticity (1999) Commun. Partial Differ. Equ., 24, pp. 1709-1730. , 1708106 0937.35137 Iftimie, D., Lopes Filho, M.C., Nussenzveig Lopes, H.J., Two dimensional incompressible ideal flow around a small obstacle (2003) Communications in Partial Differential Equations, 28 (1-2), pp. 349-379 Jin, D.Z., Dubin, D.H.E., Point vortex dynamics within a background vorticity patch (2001) Physics of Fluids, 13 (3), pp. 677-691. , DOI 10.1063/1.1343484 Lacave, C., Miot, E., Uniqueness for the vortex-wave system when the vorticity is initially constant near the point vortex (2009) SIAM J. Math. Anal., 41, pp. 1138-1163. , 2529959 1189.35259 10.1137/080737629 Lions, P.-L., (1996) Mathematical Topics in Fluid Mechanics: Incompressible Models Oxford Lecture Series in Mathematics and Its Applications, 3. , Clarendon Press Oxford 0866.76002 Lopes Filho, M.C., Nussenzveig Lopes, H.J., Xin, Z., Existence of vortex sheets with reflection symmetry in two space dimensions (2001) Arch. Ration. Mech. Anal., 158, pp. 235-257. , 1842346 1058.35176 10.1007/s002050100145 Majda, A., Bertozzi, A., (2002) Vorticity and Incompressible Flow, , Cambridge Univ. Press Cambridge 0983.76001 Marchioro, C., Pulvirenti, M., On the vortex-wave system (1991) Mechanics, Analysis, and Geometry: 200 Years after Lagrange, pp. 79-95. , M. Francaviglia (eds). Elsevier Amsterdam Marchioro, C., Pulvirenti, M., Vortices and localization in Euler flows (1993) Commun. Math. Phys., 154, pp. 49-61. , 1220946 0774.35058 10.1007/BF02096831 Marchioro, C., Pulvirenti, M., (1994) Mathematical Theory of Incompressible Nonviscous Fluids, , Springer New York 0789.76002 Newton, P., The N-vortex problem on a sphere: Geophysical mechanisms that break integrability (2010) Theor. Comput. Fluid Dyn., 24, pp. 137-149. , 1191.76027 10.1007/s00162-009-0109-6 Poupaud, F., Diagonal defect measures, adhesion dynamics and Euler equation (2002) Methods Appl. Anal., 9, pp. 533-561. , 2006604 1166.35363 Schecter, D., Two-dimensional vortex dynamics with background vorticity (2002) CP606, Non-Neutral Plasma Physics IV, pp. 443-452. , F. Anderegg (eds) et al. American Institute of Physics New York Schecter, D.A., Dubin, D.H.E., Theory and simulations of two-dimensional vortex motion driven by a background vorticity gradient (2001) Physics of Fluids, 13 (6), pp. 1704-1723. , DOI 10.1063/1.1359763 Schochet, S., The weak vorticity formulation of the 2-D Euler equations and concentration-cancellation (1995) Commun. Partial Differ. Equ., 20, pp. 1077-1104. , 1326916 0822.35111 10.1080/03605309508821124 Starovoitov, V., Uniqueness of the solution to the problem of the motion of a point vortex (1994) Sib. Mat. Zh., 35, pp. 696-701. , 1292230 Yudovich, V.I., Non-stationary flows of an ideal incompressible fluid (1963) Zh. Vyčisl. Mat. Mat. Fiz., 3, pp. 1032-1066. , 0129.19402