Artículos de revistas
Concentration Sets For 2d Incompressible Flow
Registro en:
Zamm Zeitschrift Fur Angewandte Mathematik Und Mechanik. , v. 76, n. SUPPL. 2, p. 101 - 104, 1996.
442267
2-s2.0-33749477895
Autor
Lopes-Filho M.C.
Nussenzveig Lopes H.J.
Institución
Resumen
We recall the definition of DiPerna-Majda concentration sets and their role in the study of existence for the incompressible 2D Euler equations with singular initial data. We review examples of concentration-cancellation, focusing on the issue of dynamic kinetic energy defects for the limit flows. We also describe a recent refined estimate of the dimension of (sequential) concentrations which depends on additional temporal regularity. Finally, we discuss the possibility of obtaining the temporal regularity apriori for smooth solutions and a related problem of controlling the evolution of the support of vorticity. 76 SUPPL. 2 101 104 Diperna, R., Majda, A., Reduced Hausdorff dimension and concentration-cancellation for 2-D incompressible flow (1988) J. of Amer. Math. Soc., 1, pp. 59-95 Diperna, R., Majda, A., Concentrations in regularizations for 2D incompressible flow (1987) Comm. in Pure and Appl. Math., 40, pp. 301-345 Diperna, R., Majda, A., Oscillations and concentrations in weak solutions of the incompressible fluid equations (1987) Comm. Math. Phys., 108, pp. 667-689 Delort, J.-M., Existence de nappes de tourbillon en dimension deux (1991) J. of Amer. Math. Soc., 4, pp. 553-586 Evans, L.C., Weak Convergence Methods for Nonlinear Partial Differential Equations (1990) CBMS Lecture Notes 74 Amer. Math. Soc. Greengard, C., Thomann, E., On DiPerna-Majda concentration sets for two-dimensional incompressible flow (1988) Comm. Pure Appl. Math., 41, pp. 295-303 Liu, J.-G., Xin, Z., Convergence of Vortex Methods for Weak Solutions to the 2D Euler Equations with Vortex Sheet Data, , Preprint Majda, A., Remarks on weak solutions for vortex sheets with a distinguished sign (1993) Indiana U. Math. J., 42, pp. 921-939 Nussenzveig Lopes, H.J., An estimate on the Hausdorff dimension of a concentration set for the incompressible 2-D Euler equation (1994) Ind. Univ. Math. J., 43 (2), pp. 521-534 Nussenzveig Lopes, H.J., A Refined Estimate of the Size of Concentration Sets for 2D Incompressible Inviscid Flow, , Preprint Pullin, D.I., Phillips, W.R.C., On a generalization of Kaden's problem (1981) J. Fluid Mech., 104, pp. 45-53 Vecchi, I., Wu, S., On L1-vorticity for 2-D incompressible flow (1993) Manuscripta Math., 78, pp. 403-412 Zheng, Y., Concentration-cancellation for the velocity fields in two-dimensional incompressible fluid flows (1991) Comm. Math. Phys., 135, pp. 581-594 Ziemer, W., (1989) Weakly Differentiable Functions, , New York: Springer-Verlag