Research Interests
Applied mathematics
Mathematical modelling and analysis of (non-)linear partial differential equations, nonlinear evolution equations, dynamical systems
Well-posedness, qualitative behaviour (asymptotics, singular limits) of solutions, (optimal) regularity of solutions
Free boundary problems, two-phase problems, contact angle problems
Applications in:
Mathematical fluid dynamics (e.g. incompressible Navier-Stokes)
Fluid-structure interaction problem
Thin film equation
Singular limit in continuum mechanics
Published papers
With Juan J.L. Velázquez. A thin film model for meniscus evolution. J. Math. Fluid Mech. 26:62 (2024).
With Tuhin Ghosh. Unique continuation and inverse problem for an anisotropic beam bending equation. J. Differential Equations 362 (2023).
With Barbara Niethammer, Juan J.L. Velázquez. Revisiting Shikhmurzaev's approach to the contact line problem. Acta Applicandae Mathematicae (2022).
With Hind Al Baba, Šárka Nečasová, Boris Muha. $L^p$-strong solution to fluid-rigid body interaction system with Navier slip boundary condition. J. Elliptic Parabol. Equ. (2021).
With Paul Acevedo, Chérif Amrouche, Carlos Conca. Stokes and Navier-Stokes equations with Navier boundary condition. J. Differential Equations 285 (2021).
With Chérif Amrouche, Miguel Escobedo. Semigroup theory for the Stokes operator with Navier boundary condition on $L^p$ spaces. Waves in Flows: Lecture notes in Mathematical Fluid Mechanics, Birkhauser/Springer (2021).
With Hind Al Baba Hind, Boris Muha, Šárka Nečasová. Note on the mathematical analysis of the motion of a rigid body in a generalized incompressible Navier-Stokes fluid. Conference paper: Topical Problems of Fluid Mechanics (2021).
With Chérif Amrouche, Carlos Conca, Tuhin Ghosh. $W^{1,p}$ estimates for Laplacian with Robin boundary condition in $\mathcal{C}^{1,1}$ domain. Calc. Var. PDE 59 (2020).
With Loredana Balilescu, Tuhin Ghosh. Homogenization for non-local elliptic operators in both perforated and non-perforated domains. Z. Angew. Math. Phys. 70 (2019).
PhD Thesis
Navier-Stokes equations with Navier Boundary condition (2018).