My research concerns analytical questions for nonlinear PDEs arising in fluid mechanics and control theory. I am particularly interested in compressible flows, time-periodic problems, controllability and stabilization, fluid–structure interaction, and critical-space methods.
A recurring theme in my work is the interaction between the structure of the underlying fluid model and the functional-analytic tools needed to understand its dynamics, control, and long-time behavior.
Boundary null controllability for one-dimensional barotropic and non-barotropic linearized compressible Navier–Stokes systems using a single boundary control.
Time-periodic Navier–Stokes problems in hybrid Besov spaces, with particular attention to the analytical role of cubic damping.
Existence and analysis of time-periodic solutions for the Brinkman–Forchheimer system in a Besov-space framework.
I am studying time-periodic compressible Navier–Stokes problems, with emphasis on existence, maximal regularity, stability, and the functional-analytic structure of the associated non-autonomous evolution problem.
Joint work with Kuntal Bhandari, Thomas Eiter, Šárka Nečasová, and Yoshihiro Shibata.
This project concerns a heat-conducting rigid body interacting with a compressible Navier–Stokes–Fourier fluid. The analysis combines moving-domain geometry, weak formulations, energy and entropy inequalities, compactness methods, and rigid-body dynamics.
Joint work with Kuntal Bhandari and Šárka Nečasová.
I am investigating localized insensitizing control questions for a two-dimensional chemotaxis–Brinkman system under admissible source perturbations.
This project studies sharp boundary null controllability for a two-dimensional parabolic–transport system driven by a single inflow control.
A major part of my research concerns controllability and stabilization for fluid models, especially one-dimensional compressible Navier–Stokes systems. I am interested in boundary and distributed controls, spectral obstructions, observability, and the mechanisms that determine whether a target state can be reached or stabilized.
I study PDEs driven by periodic forcing and the existence and stability of periodic responses. These questions naturally lead to evolution families, periodic propagators, maximal-regularity ideas, and fixed-point arguments for nonlinear problems.
I use Littlewood–Paley theory and Besov spaces to investigate well-posedness, nonlinear estimates, and long-time behavior near critical regularity. Transport–diffusion equations and fluid-type systems provide a natural setting for these techniques.
I am also interested in nonlinear control mechanisms beyond classical linearized controllability, including stabilization, approximate controllability, insensitizing controls, and other nonlinear control mechanisms for evolution equations.
The problems I work on draw on several complementary parts of PDE analysis and control theory.
Published papers, submitted manuscripts, and the current projects listed above are collected on the publications page.
I am building a collection of short notes on analytical tools that arise repeatedly in PDEs and control theory.