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.
Publications
- 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.
Theses