Saleh Tanveer's Home Page
Saleh Tanveer
Contact Details
tanveer@math.ohio-state.edu
Professor of Mathematics
The Ohio State University
231 West 18th Avenue
Columbus, OH 43210-1174
Office: 420 Math Tower
Office phone: 1-614-292-5710
Home phone: 1-614-791-8056
Fax: 1-614-292-1479
Research Interests
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Asymptotics beyond all orders
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Nonlinear Free boundary problems in Fluid Mechanics and Crystal Growth
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Singularities in Fluid Mechanics
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Nonlinear Partial Differential Equations in the Complex Plane
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Turbulence
Personal Information
Recent preprints
- Integral Formulation of 3-D Navier Stokes and Longer time existence of smooth solutions (with O. Costin, G.Luo), submitted
- Divergent Expansion, Borel Summability and 3-D Navier-Stokes Equation (with O. Costin, G. Luo), To appear.
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Borel Summability of Navier-Stokes equation in
R^3 and small time existence (with O. Costin), submitted.
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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).
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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)
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A note on third order structure functions in
Turbulence (with Q. Nie), Proceedings Royal Society London A 455, pp 1615-1635
(.pdf file)
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Surprises in Viscous Fingering, J. Fluid Mechanics, V. 409, pp 273-308 (.pdf file)
Recent Talks
Course Material for Au, '07
Course Material for Wi,'08
Course Material for Sp,'08
Last updated: 03/21/08
Questions? tanveer@math.ohio-state.edu