Research

On the asymptotic behavior of radial entire solutions for the equation $(-\Delta)^3 u = u^p$  in $\mathbf{R}^n$,  Journal of Differential Equations 264 (2018), pp. 3940--3975. [link to paper]

Spectral analysis  of the incompressible viscous Rayleigh-Taylor system in $\mathbf{R}^3$ (with Olivier Lafitte), Water Waves 4 (2022), pp. 259-305. [link to paper][link only to read][link to arxiv]

Linear and nonlinear analysis of the viscous Rayleigh-Taylor system with Navier-slip boundary conditions, Calc. Var. and PDEs, 63: 41 (2024). [link to hal][link to paper]

 A Liouville type result for fractional GJMS equations on higher dimensional spheres, joint with Quỳnh Lê and Quốc Anh Ngô, Calc. Var. and PDEs,  64: 39 (2025). [link to arxiv][link to paper]

Nonlinear instability of Rayleigh-Bénard convection with temperature-dependent viscosity, Z. Angew. Math. Phys., 76:156 (2025). [link to paper]

Moving sphere approach to a general weighted integral equation, joint with Quỳnh Lê, J. Math. Anal. Appl., 556 (2026) 130170. [link to paper][link to arxiv]

A necessary and sufficient condition for radial property of positive entire solutions of $\Delta^2 u+u^{-q}=0$ in $\mathbf{R}^3$, unpublished note (2019), 15 pages. [link to arxiv]

Nonlinear Rayleigh-Taylor instability of the viscous surface waves in an infinitely deep ocean (2022), 80 pages. [link to arxiv]

Influence of capillary number on nonlinear Rayleigh-Taylor instability to the Navier-Stokes-Korteweg equations (2023), 26 pages. [link to preprint] 

Nonlinear Rayleigh-Taylor instability for incompressible viscous fluid revisited (2024), 24 pages. [link to preprint]

Effect of the vertical magnetic field on Rayleigh-Taylor instability for incompressible fluids with an upper free surface (2025), 35 pages. [link to preprint]

Spectral analysis to the classical Rayleigh-Taylor instability with an upper free surface, joint with B. Barker and B. Settle, work in progress.