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), J. Functional Analysis 255 (2008) pp. 2053-2094
• 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