Saleh Tanveer

Contact Details

Research Interests

• Asymptotics beyond all orders
• Nonlinear Free boundary problems in Fluid Mechanics and Crystal Growth
• Singularities in Fluid Mechanics
• Nonlinear Partial Differential Equations in the Complex Plane
• Turbulence

Personal Information

• Curriculum Vitae

Recent preprints

• Integral Formulation of 3-D Navier Stokes and Longer time existence of smooth solutions (with O. Costin, G.Luo), submitted
• Semiclassical analysis of low and zero energy scattering for one dimensional Schrodinger operators with inverse square potentials (with O. Costin, W. Schlag, W. Staubach)
• An Integral equation Approach to Smooth 3-D Navier-Stokes Solution (with O. Costin, G. Luo) To appear.
• 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)
• Borel Summability of Navier-Stokes equation in R^3 and small time existence (with O. Costin), submitted.
• Ionization of Coulomb Systems in R^3 by time periodic forcings of arbitrary size (with O. Costin and J.L. Lebowitz), submitted.
• 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), To appear in Annales De L'Institut Henri Poincare' (C) Analyse Non Line'eaire.
• 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)

Recent Talks

• Talk at IMA, 7-17-08: A new approach to Regularity and Singularity Questions in some PDEs including 3-D Navier-Stokes.
• 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: Diverent 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.

Course Material for Au, '08

• Math 865

Personal Items

Last updated: 08/19/08

Questions? tanveer@math.ohio-state.edu