Works in preparation

• (with G. Chen, A. Kairzhan and F. Pusateri)  Global internal mode dynamics for the 1D quartic Klein-Gordon equation.

• (with N. C. Phuc) Non-blow-up of the nonlinear heat equations in the endpoint Besov space.

Publications and preprints

• (with A. Cianchi and L. Slavíková) Strongly nonlinear Robin problems for harmonic and polyharmonic functions in the half-space, Advances in Calculus of Variations, vol. 18, no. 3, 2025, pp. 773-806. Link 

• Existence and regularity of steady-state solutions of the Navier-Stokes equations arising from irregular data,  Journal of Functional Analysis, 286(9), (2024), 110364. Link

• Well-posedness for chemotaxis-fluid models in arbitrary dimensions, Nonlinearity, 35, no. 12, (2022) 6241-6283. Link

• (with H. Koch) Dirichlet problem for weakly harmonic maps with rough data, Comm. PDE. 47, (2022) 1504-1535. Link

• On the generalized parabolic Hardy-Hénon equation: Existence, blow-up, self-similarity and large-time asymptotic behavior, Differential and Integral Equations 35(1/2) (2022) 57–88. Link

• Nonlinear biharmonic equation in half-space with rough Neumann boundary data and potentials. Nonlinear Analysis, 215 (2022) 112623. Link

• On a nonlinear Laplace equation related to the boundary Yamabe problem in the upper-half-space. Comm. Pure Appl. Anal. 21(2) (2022) 517–539. Link

Talks and conferences

• June 2025 -- Harmonic Analysis and Fluid Flows  (Germany)                                                                                      

• Jan 2024 -- Hamilton University, PDE/Analysis Seminar (Canada)

• Dec 2023 -- CMS Winter Meeting, Montreal

• Nov 2023 -- Harmonic Analysis seminar, LSU (USA)

• Jan 2023 -- Oberseminar Universität Mainz (Germany)

• Mai 2022 -- Geometric Analysis Seminar, University of Pittsburgh (USA)

• Mai 2022 -- AG Nichtlineare Partielle Differentialgleichungen (KIT)

• Feb 2022 -- MPI Leipzig seminar

• Apr 2022 -- Research School on mathematical advances in geophysical flows, Marseille

• Dec 2022 -- Recent advances on nonlinear evolution equations, Winter meeting, Toronto 

• Oct 2021 -- Conference on Nonlinear Elliptic and Parabolic Partial Differential Equations (Levico Terme, Italy)

• Sep 2021 -- Conference LUBOŠ 60, in Železná Ruda, Czech Republic

• Apr 2021 -- International Prague seminar on function spaces, Charles University

• Jul 2020 -- The Analysis & PDE summer seminar, University of Minnesota, USA

• Apr 2020 -- Mathematical problems in fluid dynamics Program, Graduate seminar MSRI, Berkeley, USA