Research

Research directions and selected publications in nonlinear PDEs and mathematical physics.

Singularity formation and blow-up

Construction and classification of finite-time singularities, including Type I and Type II dynamics, refined asymptotic profiles, stability, and finite-dimensional reduction.

Blow-up profilesModulationSpectral analysisSemilinear heat equations

Fluid mechanics

Boundary-layer separation for stationary Prandtl equations and singularity mechanisms in active scalar models, with current emphasis on local profile construction and multi-region control.

PrandtlSQGBoundary layersMatched asymptotics

Complex evolution equations

Finite-time blow-up for complex Ginzburg–Landau equations and related non-variational systems, including flat profiles and regimes beyond standard self-similar scaling.

Complex Ginzburg–LandauFlat blow-upNon-variational flows

Mathematical physics

Functional and spectral inequalities for Hardy–Schrödinger operators and large quantum systems, including Cwikel–Lieb–Rozenblum and Lieb–Thirring type estimates.

Lieb–ThirringHardy operatorsMany-body theory

Selected publications

2025Finite-Rank Optimizers for the Mass-Supercritical Lieb–Thirring and Hardy–Lieb–Thirring Inequalitieswith T. M. T. Le, P. T. Nam & P.-T. Nguyen · Preprint 2025Lieb–Thirring Inequalities for Large Quantum Systems with Inverse Nearest-Neighbor Interactionswith P. T. Nam · Transactions of the AMS, in press 2025Non-Self-Similar Blowup Solutions to the Higher-Dimensional Yang–Mills Heat Flowswith A. Bensouilah & T.-E. Ghoul · Journal of Differential Equations 427
2024 Flat Blow-Up Solutions for the Complex Ginzburg–Landau Equationwith N. Nouaili & H. Zaag · Archive for Rational Mechanics and Analysis 248:117Publication link ↗ · reprint
2024Cwikel–Lieb–Rozenblum Type Inequalities for Hardy–Schrödinger Operatorswith R. L. Frank, T. M. T. Le, P. T. Nam & P.-T. Nguyen · Journal de Mathématiques Pures et Appliquées 190

Earlier publications

  • Duong Giao Ky, Van Tien Nguyen and Hatem Zaag. Construction of a stable blowup solution with a prescribed behavior for a non-scaling-invariant semilinear heat equation. Tunisian Journal of Mathematics, Vol. 1, No. 1, pp. 13-45 (2019). Publication link ↗
  • Duong Giao Ky. Profile for the imaginary part of a blowup solution for a complex-valued seminar heat equation. Journal of Functional Analysis, Vol. 277, No. 5, pp. 1531-1579 (2019). Publication link ↗
  • Duong Giao Ky. A blowup solution of a complex semi-linear heat equation with an irrational power. Journal of Differential Equations, Vol. 267, No. 9, pp. 4975-5048 (2019). Publication link ↗
  • Duong Giao Ky and Hatem Zaag. Profile of touch-down solution to a nonlocal MEMS model. Mathematical Models and Methods in Applied Sciences, Vol. 29, No. 07, pp. 1279-1348 (2019). Publication link ↗
  • Duong Giao Ky, Nejla Nouaili and Hatem Zaag. Construction of blow-up solutions for the Complex Ginzburg-Landau equation with critical parameters. Memoirs of the American Mathematical Society, Vol 285, No 1411,pp v+91, 2023. Publication link ↗
  • Duong Giao Ky, Nikos Kavallaris and Hatem Zaag. Diffusion-induced blowup solutions for the shadow limit model of a singular Gierer-Meinhardt system. Mathematical Models and Methods in Applied Sciences, Vol. 31, No. 7, pp. 1469-1503 (2021). Publication link ↗
  • Duong Giao Ky, Nejla Nouaili and Hatem Zaag. Refined asymptotic for the blow-up solution of the Complex Ginzburg-Landau equation in the subcritical case. Annales de l'Institut Henri Poincaré C - Analyse Non Linéaire, Vol. 39, No. 1 (2021). reprint
  • Giao Ky Duong, Nejla Nouaili and Hatem Zaag. Modulation theory for the flat blow-up solutions of nonlinear heat equation. Communications on Pure and Applied Analysis, Vol. 22, No. 10, pp. 2925-2959 (2023). Publication link ↗ reprint arXiv:2206.04378 ↗
  • Giao Ky Duong, Tej-Eddine Ghoul and Hatem Zaag. Gradient blowup profile for the semilinear heat equation. Discrete and Continuous Dynamical Systems, Vol. 44, No. 4, pp. 997-1025 (2024). Publication link ↗ arXiv:2109.03497 ↗
  • Giao Ky Duong, Tej-Eddine Ghoul, Nikos Kavallaris and Hatem Zaag. Blowup solutions for the shadow limit model of singular Gierer-Meinhardt system with critical parameters. Journal of Differential Equations, Vol. 336, pp. 73-125 (2019). Publication link ↗ reprint