The Ohio State University

231 West 18th Avenue

Columbus, OH 43210-1174

Office: 402 Math Tower

Office phone: 1-614-292-5710

Fax: 1-614-292-1479

- Asymptotics
- Free boundary problems
- Partial Differential Equations
- Fluid Mechanics and Turbulence

- Travelling wave states in pipe flow (with O. Ozcakir, P. Hall, E. Overman), Submitted
- Rigorous Analytical Approximation of Tritronquee solution to Painleve-I and the first singularity (with A. Adali).
- Hybrid basis scheme for computing Electrostatic fields exterior of close-to-touching discs (with D.G. Crowdy and T. Delillo) (To appear in the IMA Journal of Numerical Analysis)
- Analysis of 2+1 diffusive-dispersive PDE arising in river braiding (with C. Tsikkou)
- Analytical approximation For 2-D Nonlinear Periodic Deep Water Waves
- A quasi-solution approach to nonlinear problems--the case of Blasius similarity solution (with O. Costin. T. Kim), Fluid. Dyn. Res (46) 031419 (2014)
- Analytical approximation of Blasius' similarity solution with rigorous error bounds (with O. Costin), Siam Journal on Mathematical Analysis, 46 (6), 3782-3813 (2014)
- Proof of the Dubrovin conjecture and analysis of the tritronqu'ee solutions of P_1 (with O. Costin, M. Huang), Duke Journal of Mathematics, V 163 (4), pp 665-704 (2014).
- Existence, Uniqueness, Analyticity and Borel Summability of Boussinesq and Magnetic Benard Equations (with H. Rosenblatt)
- The lifetime of shape oscillations of a bubble in an unbounded, inviscid and compressible fluid with surfacetension (with O. Costin, M. Weinstein), SIAM J. Math. Anal, 45(5), pp 2924-2936 (2013).
- Semiclassical low energy scattering for one-dimensional Schroedinger operators with exponentially decaying potentials (with O. Costin, R. Donninger, W. Schlag), Annales Henri PoincarĂ© September 2012, Volume 13, Issue 6, pp 1371-1426
- Multiple scales in streamer discharges, with an emphasis on moving boundary approximations. (Ebert et al), Nonlinearity, 24, pp C1-C26 (2011)
- Ionization of Coulomb Systems in R^3 by time periodic forcings of arbitrary size (with O. Costin and J.L. Lebowitz), Comm. Math Physics, 296 (3), pp 681-738 (2010)
- Integral Formulation of 3-D Navier Stokes and Longer time existence of smooth solutions (with O. Costin, G.Luo), Comm. Contemp. Math, 13 (3), pp 407-462 (2011).
- Exact Results for Ionization of Model Atomic Systems (with O. Costin, J.L. Lebowitz, C. Stucchio), J. Math. Phys. 51 (1), pp 015211-1 to 015211-16 (2010)
- Semiclassical analysis of low and zero energy scattering for one dimensional Schrodinger operators with inverse square potentials (with O. Costin, W. Schlag, W. Staubach), J. Functional Analysis 255 (2008) pp. 2053-2094
- A moving boundary problem motivated by electric breakdown: I. Spectrum of linear perturbations (with L. Schafer, F.Brau, U. Ebert), Physica D, 238, 888-901 (2009).
- A moving boundary problem motivated by electric breakdown: II. Initial Value Problem (with C-Y. Kao, L. Schafer, F.Brau, U. Ebert), Physica D, 239, 1542-1559 (2010).
- Global existence for a translating near-circular Hele-Shaw bubble with surface tension (with J. Ye), SIAM. J. Math. Anal 43, pp 457-506 (2011)
- Global solutions for two-phase Hele-Shaw bubble for a near-circular initial shape (with J. Ye), Complex Variables and Elliptic Equations, 1747-6933 (2011)
- An Integral equation Approach to Smooth 3-D Navier-Stokes Solution (with O. Costin, G. Luo), Phys. Scr. T132, 014040 (2008)
- Divergent Expansion, Borel Summability and 3-D Navier-Stokes Equation (with O. Costin, G. Luo), Phil. Trans. R. Soc. A 366, pp 2775-2788 (2008)
- Short Time Existence and Borel Summability in the Navier-Stokes equation in R^3 (with O. Costin), Comm. PDEs, V 34 (8), pp 785-817 (2009)
- On a pair of interacting bubbles in planar Stokes flow (with D.G. Crowdy and G.L. Vasconcelos), J. Fluid Mech., V 541, pp231-261 (2005)
- An introduction to exponential asymptotics (with O. Costin).
- Analyzability in the context of PDEs and applications (with O. Costin), Annales de la Faculte des Sciences de Toulouse, XIII, 4, pp439-449, 2004.
- Complex Singularity Analysis for a nonlinear PDE (with O. Costin), Comm. PDEs, V 31 (4), pp 593-637 (2006)
- Nonlinear evolution PDEs in $\mathbb{R}^+ \times \mathbb{C}^d $: existence and uniqueness of solutions, asymptotic and Borel summability properties (with O. Costin), Annales De L'Institut Henri Poincare' (C) Analyse Non Line'eaire, 24 (5), pp 795-823 (2007).
- The effect of finiteness in the Saffman-Taylor viscous fingering problem (with Darren Crowdy),J. Stat. Phys.V114, pp 1501-1536
- Analyticity and nonexistence of classical steady Hele-Shaw fingers (with X. Xie), Communications on Pure and Applied Mathematics, V56, pp 353-402 (2003) (.pdf file)
- Rigorous Results in Steady Finger Selection (with X. Xie), Archives for Rational Mechanics and Analysis V166, pp 219-286 (2003) (.pdf file)
- Existence and uniqueness of solutions of nonlinear evolution systems of n-th order partial differential equations in the complex plane (with O. Costin)
- A note on third order structure functions in Turbulence (with Q. Nie), Proceedings Royal Society London A 455, pp 1615-1635 (.pdf file)
- Surprises in Viscous Fingering, J. Fluid Mechanics, V. 409, pp 273-308 (.pdf file)

- Talk at Workshop on Complex Variables and Applications, BANFF, Canada, January 13th, 2015.
- Video recording of BANFF, 2015 talk
- Applied Math Seminar, University of Illinois, Chicago, Sep. 4, 2013.
- IUTAM Conference on Vortex Dynamics, March 13, 2013
- Fluid Dynamics Seminar talk at Imperial College, January 13, 2012
- Invited talk at Free Boundary Problems, U. Nottingham, January 10, 2012
- Invited talk at BMS 11, December 22nd, 2011.
- Overview talk at Math Institute, Tohuku University, Sendai, Japan, December 12, 2011.
- Conformal map and boundary integral approach to Laplacian growth, Tohuku University, Sendai, Japan, December 12, 2011.
- Global existence and stability of translating bubbles in a Hele-Shaw cell. Tohuku University, Sendai, Japan, December 13, 2011.
- Talk at ICTP, Italy, Aug 25th, 2011: Mathematical Analysis of Floquet Problems with applications to channel and pipe flows.
- Video recording of ICTP Talk (after minute 35 onwards)
- Video recording of ICTP Talk (second half of talk)
- Talk at BIRS conference on Laplacian growth, Banff, Canada, Nov. 3, 2010
- Plenary Talk at BMS conference, Dec. 17, 2009
- Talk at Fluid Dynamics Seminar, Cambridge University, UK, October 16h, 2009
- Talk at CRM Conference on Asymptotics in dynamics, geometry and PDEs; generalized Borel summation, Pisa, Italy, October 13th, 2009
- Talk at CAMP/PDE seminar, U. Chicago, 3-11-09: A new approach to Regularity and Singularity Questions in some PDEs including 3-D Navier-Stokes.
- Talk at IMA, 7-17-08: A new approach to Regularity and Singularity Questions in some PDEs including 3-D Navier-Stokes (Video link also available below).
- Video link to IMA Talk above on 7-17-08
- Beginning Student talk (6-26-08): Divergent Series, Borel Summation and application to fluid dynamics.
- OSU Math Colloqiuum, 1-17-08: Navier-Stokes Equation--Millenium Problem.
- Talk at ICTP, Italy: Divergent Series, Borel summation and Navier Stokes Existence.
- Borel summability and Navier Stokes Existence.
- Borel summation and singularities in PDEs
- Bubbles in viscous fluid flows--Exact solutions and constraints.