Saleh Tanveer
Contact Details
tanveer@math.ohiostate.edu
Professor of Mathematics
The Ohio State University
231 West 18th Avenue
Columbus, OH 432101174
Office: 402 Math Tower
Office phone: 16142925710
Fax: 16142921479
Research Interests

Asymptotics

Free boundary problems

Partial Differential Equations

Fluid Mechanics and Turbulence
Personal Information
Recent preprints
Travelling wave states in pipe flow (with O. Ozcakir, P. Hall, E. Overman), J. Fluid Mechanics, V. 791, pp 284328 (2016).
 Travelling wave states in pipe flow (with O. Ozcakir, P. Hall, E. Overman), Expansive Uneditted Version.

Rigorous Analytical Approximation of Tritronquee solution to PainleveI and the first singularity (with A. Adali), J. Diff. Eq., (online 21 June, 2016) http://dx.doi.org/10.1016/j.jde.2016.06.009

Hybrid basis scheme for computing Electrostatic fields exterior of closetotouching discs (with D.G. Crowdy and T. Delillo), IMA J. Numer. Analysis 36 (2), pp 743769 (2016).

Analysis of 2+1 diffusivedispersive PDE arising in river braiding (with C. Tsikkou), Eur.J.Appl.Maths, published online 16th Feb, 2016; doi:10.1017/s095679251600005x

Analytical approximation For 2D Nonlinear Periodic Deep Water Waves

A quasisolution approach to nonlinear problemsthe 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), 37823813 (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 665704 (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 29242936 (2013).

Semiclassical low energy scattering for onedimensional Schroedinger operators
with exponentially decaying potentials (with O. Costin, R. Donninger, W. Schlag),
Annales Henri PoincarĂ©
September 2012, Volume 13, Issue 6, pp 13711426

Multiple scales in streamer discharges, with an emphasis on moving boundary approximations.
(Ebert et al), Nonlinearity, 24, pp C1C26 (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 681738 (2010)
 Integral Formulation of 3D Navier Stokes and Longer time existence of smooth solutions (with O. Costin, G.Luo), Comm.
Contemp. Math, 13 (3), pp 407462 (2011).
 Exact Results for Ionization of Model Atomic Systems (with O. Costin, J.L. Lebowitz, C. Stucchio), J. Math. Phys. 51 (1), pp 0152111 to 01521116 (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. 20532094
 A moving boundary problem
motivated by electric breakdown: I. Spectrum of linear perturbations
(with L. Schafer, F.Brau, U. Ebert), Physica D, 238, 888901 (2009).
 A moving boundary problem
motivated by electric breakdown: II. Initial Value Problem
(with CY. Kao, L. Schafer, F.Brau, U. Ebert), Physica D, 239, 15421559 (2010).

Global existence for a translating nearcircular HeleShaw bubble
with surface tension (with J. Ye), SIAM. J. Math. Anal 43, pp 457506 (2011)

Global solutions for twophase
HeleShaw bubble for a nearcircular initial shape (with J. Ye),
Complex Variables and Elliptic Equations, 17476933 (2011)
 An Integral equation Approach to Smooth
3D NavierStokes Solution (with O. Costin, G. Luo), Phys. Scr. T132, 014040 (2008)

Divergent Expansion, Borel Summability
and 3D NavierStokes Equation (with O. Costin, G. Luo), Phil. Trans. R.
Soc. A 366, pp 27752788 (2008)

Short Time Existence and Borel Summability in the NavierStokes equation in
R^3 (with O. Costin), Comm. PDEs, V 34 (8), pp 785817 (2009)
 On a pair of interacting bubbles
in planar Stokes flow
(with D.G. Crowdy and G.L. Vasconcelos), J. Fluid Mech., V 541, pp231261
(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, pp439449, 2004.
 Complex Singularity Analysis for a nonlinear PDE
(with O. Costin), Comm. PDEs, V 31 (4), pp 593637 (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 795823 (2007).
 The effect of finiteness in the SaffmanTaylor
viscous fingering problem (with Darren Crowdy),J. Stat. Phys.V114, pp 15011536
 Analyticity and nonexistence of classical
steady HeleShaw fingers (with X. Xie), Communications on Pure
and Applied Mathematics, V56, pp 353402 (2003) (.pdf file)
 Rigorous Results in Steady
Finger Selection (with X. Xie), Archives for Rational Mechanics and
Analysis V166, pp 219286 (2003) (.pdf file)
 Existence and uniqueness of solutions of
nonlinear evolution systems of nth 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 16151635
(.pdf file)

Surprises in Viscous Fingering, J. Fluid Mechanics, V. 409, pp 273308 (.pdf file)
Recent Talks

Talk at UCSD ME Seminar on Traveling wave states in pipe flows (May 23rd, 2016)

Video recording of Talk at Fields Institute (Jan 29th, 2016)

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 HeleShaw 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, 31109: A new approach to Regularity and Singularity Questions in
some PDEs including 3D NavierStokes.

Talk at IMA, 71708: A new approach to Regularity and Singularity Questions in
some PDEs including 3D NavierStokes (Video link also available below).

Video link to IMA Talk above on 71708

Beginning Student talk (62608):
Divergent Series, Borel Summation and application
to fluid dynamics.

OSU Math Colloqiuum, 11708: NavierStokes EquationMillenium 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 flowsExact solutions and constraints.
Course Material for Sp, '18
Last updated: 12/30/16
Questions? tanveer@math.ohiostate.edu