Math 280: Singularities in Fluid Interface Problems (Winter, 2019)

Reading List

• C. Amrouche, V. Girault, The existence and regularity of the solution of Stokes problem in arbitrary dimension, Proc. Jpn. Acad. 67(Ser. A) (1991) 171–175.
• C. Amrouche, N.E.H. Seloula, On the Stokes equations with the Navier-type boundary conditions, Differ. Equ. Appl. 3 (2011) 581–607.
• A. Castro, D. Córdoba, C. Fefferman, F. Gancedo, M. Gómez-Serrano, Finite time singularities for the free boundary incompressible Euler equations, Ann. Math. 178 (2013) 1061–1134.
• D. Coutand and S. Shkoller, On the finite-time splash and splat singularities for the 3-D free-surface Euler equations, Commun. Math. Phys., 325 , 143--183, (2014), PDF.
• D. Coutand and S. Shkoller, On the impossibility of finite-time splash singularities for vortex sheets, Arch. Rational Mech. Anal., 221 , 987--1033, (2016), PDF.
• D. Coutand and S. Shkoller, On the splash singularity for the free-surface of a Navier-Stokes fluid, (2018), Ann.I.H.Poincare–AN, PDF.
• P. Grisvard. Elliptic problems in nonsmooth domains, volume 24 of Monographs and Studies in Mathematics. Pitman (Advanced Publishing Program), Boston, MA, 1985
• C. Fefferman, A.D. Ionescu, V. Lie, On the absence of “splash” singularities in the case of two-fluid interfaces, Duke Math. J. 165 (2016) 417–462.
• V. A. Kozlov, V. G. Maz’ya, and J. Rossmann. Elliptic boundary value problems in domains with point singularities, volume 52 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 1997.
• Alois Kufner. Weighted Sobolev spaces. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1985. Translated from the Czech.