Department of Mathematics

PAPERS

As is customary in Mathematics, the order of all authors is alphabetical.

27. The strong vanishing viscosity limit with Dirichlet boundary conditions: facts, speculations, and conjectures, preprint.

26. With Hantaek Bae: Striated Regularity for the Euler Equations, preprint.

A talk on this paper from December 2015. Of particular note is a simple restatement of the result in Lagrangian coordinates. (See the corollary on page 15.)

This paper supersedes The vortex patches of Serfati, extending the result to higher dimensions, simplifying some of the proofs, and correcting a few small errors as well. The older paper includes a number of 2D examples, however.

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25. With Hantaek Bae: Propagation of regularity of level sets for a class of active transport equations, submitted.

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24. With Gung-Min Gie, Milton C. Lopes Filho, Anna Mazzucato, and Helena J. Nussenzveig Lopes: The Vanishing viscosity limit for some symmetric flows, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 36(5), 1237-1280, 2018.

Published version on ScienceDirect's website

23. With Elaine Cozzi, Well-posedness of the 2D Euler equations when velocity grows at infinity, Discrete & Continuous Dynamical Systems, 39(5), 2361-2392, 2018.

22. With Gung-Min Gie and Anna Mazzucato: Boundary layers for the Navier-Stokes equations linearized around a stationary Euler flow, Journal of Mathematical Fluid Mechanics, 20 (4), 1405-1426, 2018.

21. With Elaine Cozzi and Gung-Min Gie: The aggregation equation with Newtonian potential: The vanishing viscosity limit, Journal of Mathematical Analysis and Applications, 453(2), 841-893, 15 September 2017.

20. Observations on the vanishing viscosity limit, Transactions of the American Mathematical Society, 369, 2003-2027, 2017. Published electronically 2 June 2016. Comment.

 

Two talks related to this paper:

From December 2015 SIAM PDE meeting in Phoenix.

Recent progress on the vanishing viscosity limit in the presence of a boundary from July 2016 at the The 7th Pacific RIM Conference on Mathematics in Seoul, South Korea. This is a more general talk on the vanishing viscosity limit.

19. With Elaine Cozzi: Incompressible Euler Equations and the Effect of Changes at a Distance, Journal of Mathematical Fluid Mechanics 18(4), 765-781, 2016.

18. A characterization at infinity of bounded vorticity, bounded velocity solutions to the 2D Euler equations, Indiana University Mathematics Journal, 64(6), 1643-1666, 2015.

Version including a few more details in proofs and an afterword that includes further discussion of relation to the literature.

Talk on this paper given at SIAM PDE meeting in Orlando December 2013.

17. With David M. Ambrose, Milton C. Lopes Filho, and Helena J. Nussenzveig Lopes: Serfati solutions to the 2D Euler equations on exterior domains, Journal of Differential Equations, 259(9), 4509-4560, 2015.

Published version on ScienceDirect's website

16. With Mihaela Ignatova, Gautam Iyer, Robert L. Pego, Arghir D. Zarnescu: Global existence for two extended Navier-Stokes systems, Communications in Mathematical Sciences, 13(1), 249-267, 2015. Published version on International Press's web site.

 

Talk on this paper given in October 2012 at AMS Western Sectional Meeting in Tuscon.

15. With Gung-Min Gie: Boundary layer analysis of the Navier-Stokes equations with generalized Navier boundary condition, Journal of Differential Equations, 253(6), 1862-1892, 2012. Published version on Elsevier's web site.

Talk on this paper given in November 2011 at SIAM PDE Meeting in San Diego.

14. On the flow map for 2D Euler equations with unbounded vorticity, Nonlinearity, 24(9), 2599-2637, 2011. Published version on Nonlinearity's web site. Comment

Talk on the first part of this two-part paper given in December 2009 at SIAM PDE Meeting in Miami. This first part is a refinement of the fourth chapter of my thesis.

Talk on the second part of this paper given in June 2011 at the 3rd Workshop on Fluids and PDE in Campinas, Brazil. This second part is very hard to give a talk on, as it is examines an inverse problems more closely tied to the theory of functional equations than to classical fluid mechanics, so the techniques are unfamiliar to most of the intended audience. (The second part of this paper is, admittedly, idiosyncratic.)

13. With Roger Temam and Xiaoming Wang: Boundary layer associated with the Darcy-Brinkman-Boussinesq model for convection in porous media, Physica D: Nonlinear Phenomena, 240(7), 619-628, 2011. Published version on Elsevier's web site.

Talk on this paper given in October 2010 at AMS Western Sectional Meeting in UCLA.

12. Eigenvalues of the Stokes operator versus the Dirichlet Laplacian for a bounded domain in the plane, Pacific Journal of Mathematics, 244(1): 99-132, 2010. Published versions on PJM's web site: for screen, for print.

11. Infinite-energy 2D statistical solutions to the equations of incompressible fluids, Journal of Dynamics and Differential Equations, 21(4): 631-661, 2009. Published version on Springer's web site.

10. With Milton C. Lopes Filho and Helena J. Nussenzveig Lopes: Vanishing viscosity limit for an expanding domain in space, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 26(6): 2521-2537, 2009. Published version can be found here.

9. On the vanishing viscosity limit in a disk, Mathematische Annalen, 343:701-726, 2009. Published version on Springer's web site.

8. With Dragoş Iftimie: Remarks on the vanishing obstacle limit for a 3D viscous incompressible fluid, Proceedings of the American Mathematical Society, 137(2):685-694, 2009. Published version on AMS's web site.

7. Vanishing viscosity and the accumulation of vorticity on the boundary, Communications in Mathematical Sciences, 6(4):869-880, 2008. Comment. Bonus: some further, simple observations.

6. With Riad Masri: Analytic continuation of multiple Hurwitz zeta functions, Mathematical Proceedings of the Cambridge Philosophical Society, 145(3):605-617, 2008.

5. Expanding domain limit for incompressible fluids in the plane, Communications in Mathematical Physics, 278(3):753-773, 2008. Published version (on Springer's web site). Comment. Comment on title.

4. With Elaine Cozzi: Vanishing Viscosity in the plane for vorticity in borderline spaces of Besov type, Journal of Differential Equations, 235(2):647-657, 2007. Published version (on Elsevier's web site), Comment.

3. On Kato's conditions for vanishing viscosity, Indiana University Mathematics Journal, 56(4):1711-1721, 2007. Published version (on IUMJ's web site).

2. Navier-Stokes equations with Navier boundary conditions for a bounded domain in the plane, SIAM Journal on Mathematical Analysis, Vol 38(1):210-232, 2006. Published version (on SIAM's web site), Comments.

1. The Inviscid Limit for Two-Dimensional Incompressible Fluids with Unbounded Vorticity, Mathematical Research Letters, Vol 11(4):519-528, 2004.