SUMMER SCHOOL
Fluid Dynamics

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Topics for the participants' lectures

Each participant will lecture on one of the following papers. Some of the papers are longer and will be discussed by two of the participants. Some of the papers will only be read partially, more detailed instructions will be given at the time of assignment of topics. The papers are not listed in the order of difficulty nor in the order they will be presented.

Every participant will lecture for 2 hours, split into two lectures at different days.

  1. On the collapse of tubes carried by 3D flow, (D. Cordoba, C. Fefferman, preprint on arXiv server [Burak Erdogan]

  2. Remarks on the breakdown of smooth solutions for the 3D Euler equations (T. Beale, T. Kato, A. Majda) (Comm. Math. Phys. 94, pp. 61-66 (1984)) This may be supplemented by the corresponding BMO result in "Bilinear estimates in BMO and the Navier Stokes equations" (Kozono, Taniuchi, Math. Z. 235 pp 173-194 (2000)) [Natasa Pavlovic]

  3. Geometric constraints on potentially singular solutions for the 3D Euler equations (P. Constantin, C. Fefferman, A. Majda) (Comm. in Part. Diff. Eq. 21 (3&4) pp 559-571 (1996) [Stephanie Molnar]

  4. Non-existence of simple hyperbolic blow-up for the quasi-geostrophic equation (D. Cordoba) (Annals of Math. 148 pp 1135-1152 (1998) [Chiu-Yen Kao]

  5. Well-posedness for the Navier-Stokes equations (H. Koch, D. Tataru) preprint [Chan Woo Yang]

  6. A bilinear estimate with applications to the KdV equation (C. Kenig, G. Ponce, L. Vega) Journal of the AMS 9 (no. 2) 1996 99. 573-603 PART I: pp 573-586 [Xiaochun Li]

  7. A bilinear estimate with applications to the KdV equation (C. Kenig, G. Ponce, L. Vega) Journal of the AMS 9 (no. 2) 1996 99. 573-603 PART II: pp 586-590 (this part requires some extra reading in references [15] and [18] of this paper) [Alexei Novikov]

  8. Well-posedness in Sobolev spaces of the full water wave problem in 2D (S. Wu) Invent. Math. 130 (no 1) 39-72 (1997) PART I : pp 39-52 [Asger Tornquist]

  9. Well-posedness in Sobolev spaces of the full water wave problem in 2D (S. Wu) Invent. Math. 130 (no 1) 39-72 (1997) PART II: pp 53-72 (beginning with section "Wellposedness of the quasilinear system") [Camil Muscalu]

  10. Ekman layers of rotating fluids, the case of well prepared initial data (E. Grenier, N. Masmoudi) Comm. in Part. Diff. Eq. 22(5&6) pp 953-975 (1997) [Silvius Klein]

  11. A cheap Caffarelli-Kohn-Nirenberg inequality for Navier Stokes equation with hyper dissipation (N. Katz, N. Pavlovic) preprint on arXiv server [Ya-Ju Tsai]