Deutsch Intern
Mathematics in the Sciences

Francesco De Anna

Dr. Francesco De Anna

Lecturer
Chair of Mathmatics VI
Emil-Fischer-Straße 40
97074 Würzburg
Building: 40 (Mathematik Ost)
Room: 03.008
Phone: +49 931 31-81550
Fax: +49 931 31-80944

 

 

Portrait Francesco DeAnna

Preprints
  • F. De Anna, J. Kortum, and S. Scrobogna. Quantitative aspects on the ill-posedness of the Prandtl and hyperbolic Prandtl equations. 2023.arXiv:2305.04664
  • F. De Anna, C. Liu, A. Schlömerkemper, J.-E. Sulzbach: Temperature dependent extensions of the Cahn-Hilliard equation,  arXiv:2112.14665

 

Publikationen
  • L. Bachmann, F. De Anna, A. Schlömerkemper, and Y. Şengül. Existence of solutions for stress-rate type strain-limiting viscoelasticity in Gevrey spaces. Philos. Trans. A Math. Phys. Eng. Sci., 381(2263):20220374, 2023. DOI: 10.1098/rsta.2022.0374
  • N. Aarach, F. De Anna, M. Paicu, and N. Zhu. On the role of the displacement current and the Cattaneo's law on boundary layers of plasma. J. Nonlinear Sci., 33(6): Paper No. 112, 51, 2023. DOI: 10.1007/s00332-023-09966-2
  • F. De Anna, J. Kortum, and S. Scrobogna. Gevrey-class-3 regularity of the linearised hyperbolic Prandtl system on a strip. J. Math. Fluid Mech., 25(4): Paper No. 80, 28, 2023. DOI: 10.1007/s00021-023-00821-8
  • F. De Anna and H. Wu. Uniqueness of global weak solutions for the general Ericksen-Leslie system with Ginzburg-Landau penalization in T^2. Calc. Var. Partial Differential Equations, 62(5): Paper No. 157, 79, 2023. DOI: 10.1007/s00526-023-02493-8
  • F. De Anna, J. Kortum, and A. Schlömerkemper. Struwe-like solutions for an evolutionary model of magnetoviscoelastic fluids. J. Differential Equations, 309:455–507, 2022. DOI: 10.1016/j.jde.2021.11.034
  • F. De Anna and M. Paicu. The Fujita-Kato theorem for some Oldroyd-B model. J. Funct. Anal., 279(11):108761, 64, 2020. DOI: 10.1016/j.jfa.2020.108761
  • F. De Anna and S. Scrobogna. A global well-posedness result for the Rosensweig system of ferrofluids. Rev. Mat. Iberoam., 36(3):895–938, 2020. DOI: 10.4171/rmi/1153.
  • F. De Anna and C. Liu. Non-isothermal general Ericksen-Leslie system: derivation, analysis and thermodynamic consistency. Arch. Ration. Mech. Anal., 231(2):637–717, 2019. DOI: 10.1007/s00205-018-1287-4
  • F. De Anna and F. Fanelli. Global well-posedness and long-time dynamics for a higher order quasi-geostrophic type equation. J. Funct. Anal., 274(8):2291–2355, 2018. DOI: 10.1016/j.jfa.2017.10.017
  • F. De Anna and A. Zarnescu. Global well-posedness and twist-wave solutions for the inertial Qian-Sheng model of liquid crystals. J. Differential Equations, 264(2):1080–1118, 2018. DOI: 10.1016/j.jde.2017.09.031
  • F. De Anna. Global solvability of the inhomogeneous Ericksen-Leslie system with only bounded density. Anal. Appl. (Singap.), 15(6):863–913, 2017. DOI: 10.1142/S0219530516500172.
  • F. De Anna. A global 2D well-posedness result on the order tensor liquid crystal theory. J. Differential Equations, 262(7):3932–3979, 2017. DOI: 10.1016/j.jde.2016.12.006.
  • F. De Anna and A. Zarnescu. Uniqueness of weak solutions of the full coupled Navier-Stokes and Q-tensor system in 2D. Commun. Math. Sci., 14(8):2127–2178, 2016. DOI: 10.4310/CMS.2016.v14.n8.a3.
  • F. De Anna. Global weak solutions for Boussinesq system with temperature dependent viscosity and bounded temperature. Adv. Differential Equations, 21(11-12):1001–1048, 2016. Available at: http://projecteuclid.org/euclid.ade/1476369295
  • F. Cardin, F. De Anna, and C. Tebaldi. Stationary solutions for forced reduced MHD on the 2-torus. J. Math. Anal. Appl., 403(2):599–605, 2013. DOI: 10.1016/j.jmaa.2013.02.053

Research interest

My research activity is on the analysis and modeling of several complex fluids. The core of my research is on the study of partial differential equations and their applications to the fluidodynamics of anisotropic materials. 

In particular, my results have endorsed the flow perception of liquid crystals, both in the director theory of the Ericksen–Leslie formalism as well as in the Q-tensor framework introduced by de Gennes and developed by Beris and Edwards. 

A significant amount of effort has been devoted to the dynamics of non-isothermal complex fluids, the physics of which is entirely determined by an extension of the energetic variational approach (EnVarA), in accordance with the main laws of thermodynamics. 

The arising problems involve also other fields such as harmonic analysis, functional analysis and, above all, Littlewood-Paley theory and paradifferential calculus.

 

Keywords
  • Fluid Dynamics: complex fluids, non-isothermal fluids, liquid crystals, variable viscosity. 
  • Modeling techniques: Energetic Variational Approach. 
  • PDEs: director theory, Q-tensor theory, Boussinesq system. 
  • Harmonic analysis toolbox: Fourier analysis, Littlewood-Paley decomposition, paradifferential calculus, logarithmic estimates.

Current
  • Exercises in Analysis in Several Variables (Fundamentals of Analysis 2), in groups, 2 hours, Thu 16-18, Fri 10-12
  • Exercises in Analysis 2, In groups, 2 hours, Mon 10-12,12-14,14-16; Tue 10-12,14-16,16-18; Wed 12-14
 
Past Courses
  • Winter semester 20/21: Exercises in Analysis in One Variable (Foundations of Analysis 1)
  • Summer semester 20: Exercises for the introduction to Partial Differential Equations