Research

Research interest

My work lies at the intersection of nonlinear partial differential equations (PDEs) and their applications to fluid mechanics. Broadly, I am interested in how fluids evolve, interact and organize — both at a rigorous theoretical level and through computations.

My research spans three complementary realms:

• Modeling of fluids: I study how mathematical models of fluids are derived using relaxation techniques and asymptotic limits, with an emphasis on ensuring that these models remain physically relevant and thermodynamically consistent.

• Mathematical analysis of PDEs: I study the existence of weak solutions via entropy methods, as well as uniqueness, stability and long-time behavior using tools such as the relative entropy method. Besides this, I am interested in regularity conditions under which solutions conserve their energy/entropy, which connects to the study of anomalous dissipation.

• Computations and applications: I explore geophysical and environmental fluid systems, including oceanic and atmospheric dynamics, plankton and coral ecosystems, and data-driven approaches. These computational directions complement the theoretical analysis, bridging rigorous PDE theory with real-world applications.

Applications of my research include compressible gases, multicomponent mixtures, anomalous dissipation, degenerate diffusion and related fluid models.

Journal papers

1. Berselli, L.C., Georgiadis, S., Tzavaras, A.E. Absence of anomalous dissipation for weak solutions of the Maxwell-Stefan system. Nonlinearity 38, 025018 (2025). (see https://iopscience.iop.org/article/10.1088/1361-6544/ada7b8 or arXiv[2407.10134])

2. Georgiadis, S. Energy identity for the incompressible Cahn-Hilliard/Navier-Stokes system with non–degenerate mobility. Z. Angew. Math. Phys. 75, 174 (2024). (see https://doi.org/10.1007/s00033-024-02312-w or arXiv[2408.01749])

3. Georgiadis, S., Jüngel, A. Global existence of weak solutions and weak-strong uniqueness for nonisothermal Maxwell-Stefan systems, Nonlinearity 37, 075016 (2024). (see DOI: 10.1088/1361-6544/ad4c49 or arXiv[2303.17693])

4. Georgiadis, S., Tzavaras, A.E. Alignment via friction for nonisothermal multicomponent fluid systems, Acta Appl. Math. 191, 3 (2024). (see https://doi.org/10.1007/s10440-024-00655-0 or arXiv[2311.10546])

5. Berselli, L.C., Georgiadis, S. Three results on the energy conservation for the 3D Euler equations, Nonlinear Differ. Equ. Appl. 31, 33 (2024). (see https://doi.org/10.1007/s00030-024-00924-9 or arXiv[2307.04410])

6. Georgiadis, S., Tzavaras, A.E. Asymptotic derivation of multicomponent compressible flows with heat conduction and mass diffusion, ESAIM: Math. Model. Numer. Anal. 57 (2023), 69–106.  (see  https://doi.org/10.1051/m2an/2022065 or arXiv[2112.13625])

Books

1. Coming soon...

Proceedings papers

1. Georgiadis, S. , Jüngel, A., Tzavaras, A.E. Non-isothermal multicomponent flows with mass diffusion and heat conduction, In: Parés, C., Castro, M.J., Morales de Luna, T., Muñoz-Ruiz, M.L. (eds) Hyperbolic Problems: Theory, Numerics, Applications. Volume I. HYP 2022. SEMA SIMAI Springer Series, vol 34. Springer, Cham. (see https://doi.org/10.1007/978-3-031-55260-1_19 or arXiv[2301.08928])

Preprints

1. Georgiadis, S., Kim, H., Tzavaras, A.E. Renormalized solutions for the Maxwell-Stefan system with an application to uniqueness of weak solutions. (see arXiv[2311.10465])

2. Coming soon...

Collaborators

• Athanasios Tzavaras, KAUST, Saudi Arabia 🇸🇦 

• Ansgar Jüngel, TU Wien, Austria 🇦🇹 

• Hoyoun Kim, KAUST, Saudi Arabia 🇸🇦 

• Luigi Berselli, Università di Pisa, Italy 🇮🇹

• Stefano Spirito, Università degli Studi dell'Aquila, Italy 🇮🇹