Aynur Bulut

[Photo]

Associate Professor

Department of Mathematics
Louisiana State University
224 Lockett Hall

aynurbulut (at) lsu.edu

My work focuses on the study of nonlinear partial differential equations, with an emphasis on the analysis of long-time behavior for dispersive PDE in supercritical settings and related fluid models.

Research (show/hide)

A. Bulut and H. Dong.
Global well-posedness for supercritical SQG with perturbations of radially symmetric data.

A. Bulut, M.K. Huynh, and S. Palasek.
Non-uniqueness up to the Onsager threshold for the forced SQG equation.

A. Bulut, M.K. Huynh, and S. Palasek.
Convex integration for the forced Euler equations above the Onsager exponent.

A. Bulut, M.K. Huynh, and S. Palasek.
Epochs of regularity for wild Hölder-continuous solutions of the Hypodissipative Navier-Stokes System.

A. Bulut.
Non-existence of splash singularities for the two-fluid Euler--Navier-Stokes system.

A. Bulut.
Probabilistic local and global well-posedness for the nonlinear wave equation on B₂ × T.

A. Bulut and K.M. Huynh.
A geometric trapping approach to global regularity for 2D Navier-Stokes on manifolds.
Mathematical Research Letters 30 (2023), no. 4, 969--1010.

A. Bulut.
Blow-up criteria below scaling for defocusing energy-supercritical NLS and quantitative global scattering bounds.
American Journal of Mathematics 145 (2023), no. 2, 543--567.

A. Bulut and H. Dong.
Nonlinear instability for the surface quasi-geostrophic equation in the supercritical regime.
Communications in Mathematical Physics 384 (2021), 1679--1707.

A. Bulut and B. Dodson.
Global well-posedness for the logarithmically energy-supercritical Nonlinear Wave Equation with partial symmetry.
International Mathematics Research Notices (2021), no. 8, 5943--5967.

A. Bulut.
Negative energy blowup results for the focusing Hartree hierarchy via identities of virial and localized virial type.
Comm. Par. Diff. Eq. 43 (2018), no. 9, 1281--1305.

A. Bulut.
An optimal decay estimate for the linearized water wave equation in 2D.
Proceedings of the American Mathematical Society 144 (2016), no. 11, 4733-4742.

J. Bourgain and A. Bulut.
Almost sure global well posedness for the radial nonlinear Schrödinger equation on the unit ball I: the 2D case.
Annales Institut Henri Poincare (C) (2013), http://dx.doi.org/10.1016/j.anihpc.2013.09.002.

J. Bourgain and A. Bulut.
Invariant Gibbs measure evolution for the radial nonlinear wave equation on the 3D ball.
Journal of Functional Analysis 266 (2014), no. 4, 2319-2340.

J. Bourgain and A. Bulut.
Almost sure global well posedness for the radial nonlinear Schrödinger equation on the unit ball II: the 3D case.
Journal of the European Mathematical Society 16 (2014), 1289-1325.

J. Bourgain and A. Bulut.
Gibbs measure evolution in radial nonlinear wave and Schrödinger equations on the ball.
Comptes Rendus Mathematique 350 (2012) 11-12, 571-575.

A. Bulut.
The defocusing cubic nonlinear wave equation in the energy-supercritical regime.
Recent Advances in Harmonic Analysis and Partial Differential Equations, 12-22, Contemp. Math 581, Amer. Math. Soc., Providence, RI 2012.

A. Bulut.
The defocusing energy-supercritical cubic nonlinear wave equation in dimension five.
Transactions of the American Mathematical Society 367 (2015), 6017--6061.

A. Bulut.
The radial defocusing energy-supercritical cubic nonlinear wave equation in R^{1+5}.
Nonlinearity 27 (2014), 1859-1877.

A. Bulut.
Global well-posedness and scattering for the defocusing energy-supercritical cubic nonlinear wave equation.
Journal of Functional Analysis 263 (2012), no. 6, 1609-1660.

A. Bulut, M. Czubak, D. Li, N. Pavlovic and X. Zhang.
Stability and unconditional uniqueness of solutions for energy-critical wave equations in high dimensions.
Communications in Partial Differential Equations 38 (2013) no. 4, 575-607.

A. Bulut.
Maximizers for the Strichartz inequalities for the wave equation.
Differential and Integral Equations 23 (2010), 1035-1072.

A. Bulut.
Global well-posedness and scattering for the defocusing energy-supercritical cubic nonlinear wave equation.
2011, Ph.D. Thesis, The University of Texas at Austin.

A. Bulut.
Aspects of the structure of the second dual algebras.
2005, M.S. Thesis, Bogazici University.

Teaching

Invited Talks

Seminars
- Applied Analysis Seminar
- Colloquium