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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: 03.020

 

 

Portrait Francesco DeAnna

Publications
  • F. De Anna, M. Paicu, The Fujita-Kato theorem for some Oldroyd-B model, J. Funct. Anal., 279, 11 (2020)
  • F. De Anna, S. Scrobogna, A global well-posedness result for the Rosensweig system of ferrofluids. Rev. Mat. Iberoam. Electronically published on January 3, 2020 (to appear in print
  • F. De Anna, C. Liu, Non-isothermal general Ericksen-Leslie system: derivation, analysis and thermodynamic consistency, Arch. Ration. Mech. Anal., 231, (2019) 637–717 
  • F. De Anna, F. Fanelli, Global well-posedness and long-time dynamics for a higher order Quasi-Geostrophic type equation, J. Funct. Anal., 274 (2018), 2291-2355
  • F. De Anna, A. Zarnescu, Global well-posedness and twist-wave solutions for the inertial Qian-Sheng model of liquid crystals, J. Differ. Equations, 264, 2 (2018), 1080-1118
  • F. De Anna, A global 2D well-posedness result on the order tensor liquid crystal theory, J. Differ. Equations, 262, 8 (2017), 3932-3979
  • F. De Anna, Global solvability of the inhomogeneous Ericksen-Leslie system with only bounded density, Anal. Appl., 0 (2016), 1-51
  • F. De Anna, Global weak solutions for Boussinesq system with temperature dependent viscosity and bounded temperature, Adv. Differential Equ., 21 (2016), no. 11/12, 1001-1048
  • F. De Anna, A. Zarnescu, Uniqueness of weak solutions of the full coupled Navier-Stokes and Q-tensor system in 2D, Comm. Math. Sci., 14 (2016), 2127-2178
  • F. Cardin, F. De Anna, C. Tebaldi, Stationary solutions for forced Reduced MHD on the 2-torus, J. Math. Anal. Appl. 403 (2013) 599-605

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