Nuno J. Alves
- Postdoctoral Research Fellow, Applied Mathematics and Computational Science
Biography
Nuno J. Alves is a postdoctoral researcher in the Free Boundary and Interface Problems group, led by Prof. José Miguel Urbano. He earned his PhD in Applied Mathematics and Computational Science from KAUST in 2023, under the supervision of Prof. Athanasios E. Tzavaras. Before returning to KAUST in March 2026, he was a postdoctoral researcher at the University of Vienna, working with Prof. Peter Markowich. His research lies broadly in mathematical analysis, with particular emphasis on functional analysis, harmonic analysis, the calculus of variations, and the analysis of partial differential equations.
Research Interests
Nuno Alves’ research focuses on mathematical analysis and its applications to nonlinear partial differential equations. His interests include functional and harmonic analysis, compactness and convergence in function spaces, fractional integral operators, asymptotic problems for PDEs, and Gamma-convergence methods in the calculus of variations. His work also involves fluid and kinetic models, including Euler-type, BGK-type, and Vlasov-type equations, with an emphasis on stability, singular limits, weak-strong uniqueness, and relative entropy methods.
Education
- Doctor of Philosophy (Ph.D.)
- Applied Mathematics and Computational Science, King Abdullah University of Science and Technology, Saudi Arabia, 2023
- Master of Science (M.S.)
- Mathematics and Applications, Instituto Superior Técnico, Portugal, 2017
- Bachelor of Science (B.S.)
- Applied Mathematics and Computational Science, Instituto Superior Técnico, Portugal, 2015
Selected Publications
- N. J. Alves, L. Grafakos, and A. E. Tzavaras, A bilinear fractional integral operator for Euler–Riesz systems, Analysis & PDE, to appear.
- N. J. Alves, J. Haskovec, Rigorous dense graph limit of a model for biological transportation networks, SIAM Journal on Mathematical Analysis, to appear.
- N. J. Alves, Kolmogorov–Riesz compactness in asymptotic $L_p$ spaces, Proceedings of the American Mathematical Society, to appear.
- N. J. Alves, L. Grafakos, Uniform boundedness of parametric bilinear fractional integrals, Annales Fennici Mathematici, to appear.
- N. J. Alves, On F-spaces of almost-Lebesgue functions, Acta Mathematica Hungarica 176(2), 365–386, 2025.
- N. J. Alves, A. E. Tzavaras, Zero-electron-mass and quasi-neutral limits for bipolar Euler–Poisson systems, Zeitschrift für Angewandte Mathematik und Physik 75(1), 17, 2024.
- N. J. Alves, A. E. Tzavaras, The relaxation limit of bipolar fluid models, Discrete and Continuous Dynamical Systems 42(1), 211–237, 2022.
Recent Works
- N. J. Alves, A truncation criterion for compactness in asymptotic $L_p$ spaces, arXiv.
- N. J. Alves, J. M. Urbano, An $L^1$-theory for $p$-Schrödinger equations with confinement in measure, arXiv.
- N. J. Alves, Isometries and geometric liftings for Alexiewicz-normed $L^\infty$ spaces, arXiv.
- N. J. Alves, From nonisothermal BGK to Euler Maxwellians via relative entropy, arXiv.
- N. J. Alves, P. Markowich, and A. E. Tzavaras, Local analytic well-posedness for one-dimensional Vlasov–Dirac–Benney-type equations, arXiv.