MAT1638: Fluids dynamics

Possible topics for oral presentations

You are welcome to find any paper that interests you and that is related to fluid dynamics.

Some possibilities are listed below, with links in some cases. Most of them are reviewed on Mathscinet, and in most cases you can probably find an electronic copy, or a hard copy, through the University Library. If not, please let me know and I can help you track down a copy.

Please feel free to discuss any possibilities with me, and please let me know what you have in mind (so that we do not end up with two people giving presentations on the same paper).

• Ambrosetti, A. and Struwe, M., "Existence of steady vortex rings in an ideal fluid." Arch. Rational Mech. Anal. 108 (1989), no. 2, 97-109

• Benedetto, D., Caglioti, E., and Marchioro, C., "On the motion of a vortex ring with a sharply concentrated vorticity." Math. Methods Appl. Sci. 23 (2000), no. 2, 147-168.

• Marchioro, Carlo and Pulvirenti, Mario, "Vortices and localization in Euler flows." Comm. Math. Physa. 154 (1993), no. 1, 49-61.

• Koch, Herbert and Tataru, Daniel, "Well-posedness for the Navier-Stokes equations." Adv. Math. 157 (2001), no. 1, 22-35.

• Necas, J., Ruzicka, M., and Sverak, V, "On Leray's self-similar solutions of the Navier-Stokes equations." Acta Math. 176 (1996), no. 2, 283-294.

• Kiselev, A. and Sverak, V., "Small scale creation for solutions of the incompressible two-dimensional Euler equation." Ann. of Math. (2) 180 (2014), no. 3, 1205-1220.

• Escauriaza, L., Seregin, G., and Sverak, V., " Backward uniqueness for parabolic equations." Arch. Ration. Mech. Anal. 169 (2003), no. 2, 147-157.

• Seregin, Gregory and Sverak, Vladimir, "The Navier-Stokes equations and backward uniqueness." Nonlinear problems in mathematical physics and related topics, II, 353-366, Int. Math. Ser. (N. Y.), 2, Kluwer/Plenum, New York, 2002.

• Chemin, Jean-Yves and Zhang, Ping, "Remarks on the global solutions of 3-D Navier-Stokes system with one slow variable." Comm. Partial Differential Equations 40 (2015), no. 5, 878-896.

• Caffarelli, L., Kohn, R., and Nirenberg, L., "Partial regularity of suitable weak solutions of the Navier-Stokes equations." Comm. Pure Appl. Math. 35 (1982), no. 6, 771–831.

• Other papers by Sverak and collaborators.

• Papers by de Lellis, Szelekyhidi and collaborators, other than those to be discussed in the lectures (which are Ann Math 2009 and Inventiones 2013).

• Terence Tao's preprint http://arxiv.org/abs/1402.0290.

• the preprint http://arxiv.org/abs/1307.0565, by Phil Isett.