212 citations · 848 across the 74 of their papers we have counts for
24 papers · 1 filter
Borel summability of Navier-Stokes equation in and small time existence
O. Costin, S. Tanveer
We consider the Navier-Stokes initial value problem, $$v_t - \nabla v = -\mathcal{P} [ v \cdot \nabla v \right ] + f, v(x, 0) = v_0 (x), x \in \mathbb{R}^3 $$ where i…
Global reconstruction of analytic functions from local expansions
O. Costin, X. Xia
A new summation method is introduced to convert a relatively wide family of infinite sums and local expansions into integrals. The integral representations yield global information…
Ionization of Coulomb systems in $\RR^3$ by time periodic forcings of arbitrary size
O. Costin, J. L. Lebowitz, S. Tanveer
We analyze the long time behavior of solutions of the Schrödinger equation , $x\in\RR^3$, , describing a Coulomb system subjected to a spatially compa…
On the proof of universality for orthogonal and symplectic ensembles in random matrix theory
Ovidiu Costin, Percy Deift, Dimitri Gioev
We give a streamlined proof of a quantitative version of a result from [DG1] which is crucial for the proof of universality in the bulk [DG1] and also at the edge [DG2] for orthogo…
Ionization in a 1-Dimensional Dipole Model
O. Costin, J. L. Lebowitz, C. Stucchio
We study the evolution of a one dimensional model atom with -function binding potential, subjected to a dipole radiation field with a -periodic real-valued…
Resurgence of the Kontsevich-Zagier power series
Ovidiu Costin, Stavros Garoufalidis
The paper is concerned with the Kontsevich-Zagier formal power series and its analytic properties. To begin with, we give an explicit…
Exact Results for the Ionization of a Model Quantum System
O. Costin, A. Rokhlenko, J. Lebowitz
We prove that a model atom having one bound state will be fully ionized by a time periodic potential of arbitrary strength r and frequency omega. Starting with the system in the bo…
Nonperturbative analysis of a model quantum system under time periodic forcing
O. Costin, R. D. Costin, A. Rokhlenko J. Lebowitz
We analyze the time evolution of a one-dimensional quantum system with an attractive delta function potential whose strength is subjected to a time periodic (zero mean) parametric…
Exponential asymptotics, transseries, and generalized Borel summation for analytic rank one systems of ODE's
O. Costin
For analytic nonlinear systems of ordinary differential equations, under some non-degeneracy and integrability conditions we prove that the formal exponential series solutions (tra…
Rigorous WKB for finite order linear recurrence relations with smooth coefficients
O. Costin, R. D. Costin
We study the behavior of recurrence relations of the type $k\in \zdd$ ( fixed). The are functions in each variable…
Optimal uniform estimates and rigorous asymptotics beyond all orders for a class of ODE's
O. Costin, M. D. Kruskal
For first order differential equations of the form and second order homogeneous linear differential equations with locally integrab…
On optimal truncation of divergent series solutions of nonlinear differential systems; Berry smoothing
O. Costin, M. D. Kruskal
We prove that for divergent series solutions of nonlinear (or linear) differential systems near a generic irregular singularity, the common prescription of summation to the least t…
On Borel summation and Stokes phenomena of nonlinear differential systems
O. Costin
In this paper we study analytic (linear or) nonlinear systems of ordinary differential equations, at an irregular singularity of rank one, under nonresonance conditions. It is show…
Time asymptotics of the Schroedinger wave function in time-periodic potentials
O. Costin, R. D. Costin, J. L. Lebowitz
We study the transition to the continuum of an initially bound quantum particle in $\RR^d$, , subjected, for , to a time periodic forcing of arbitrary magnitude. T…
Movable singularities of solutions of difference equations in relation to solvability and a study of a superstable fixed point
O. Costin, M. D. Kruskal
A unique analytic continuation result is proven for solutions of a relatively general class of difference equations by using techniques of generalized Borel summability. We overvie…
Rigorous bounds of Stokes constants for some nonlinear ODEs at rank one irregular singularities
O. Costin, R. D. Costin, M. Kohut
A rigorous way to obtain sharp bounds for Stokes constants is introduced and illustrated on a concrete problem arising in applications.
Borel summation of adiabatic invariants
O. Costin, L. Dupaigne, M. D. Kruskal
Borel summation techniques are developed to obtain exact invariants from formal adiabatic invariants (given as divergent series in a small parameter) for a class of differential eq…
Analyzability in the context of PDEs and applications
O. Costin, S. Tanveer
We discuss the notions of resurgence, formalizability, and formation of singularities in the context of partial differential equations. The results show that Ecalle's how analyzabi…
Topological construction of transseries and introduction to generalized Borel summability
O. Costin
Transseries in the sense of Écalle are constructed using a topological approach. A general contractive mapping principle is formulated and proved, showing the closure of transserie…
Analytic methods for obstruction to integrability in discrete dynamical systems
O. Costin, M. D. Kruskal
A unique analytic continuation result is proved for solutions of a relatively general class of difference equations, using techniques of generalized Borel summability. This continu…
Singularity barriers and Borel plane analytic properties of 1+ difference equations
O. Costin
The paper addresses generalized Borel summability of ``'' difference equations in ``critical time''. We show that the Borel transform of a prototypical such equation is an…
Nonlinear Stokes phenomena in first or second order differential equations
O. Costin
We study singularity formation in nonlinear differential equations of order , . We assume is analytic at and $\partial_y A(0,0)=λ\ne…
Nonlinear evolution PDEs in R^+ \times C^d: existence and uniqueness of solutions, asymptotic and Borel summability
O. Costin, S. Tanveer
We consider a system of -th order nonlinear quasilinear partial differential equations of the form $${\bf u}_t + \mathcal{P}(\partial_{\bf x}^{\bf j}){\bf u}+{\bf g} \left( {\bf…
Borel summability and Lindstedt series
O. Costin, G. Gallavotti, G. Gentile +1
Resonant motions of integrable systems subject to perturbations may continue to exist and to cover surfaces with parametric equations admitting a formal power expansion in the stre…