Lorenzo Brandolese

Address:

https://orcid.org/0000-0002-3045-0016

Enseignement

Curriculum Vitae

Main research interests

• Asymptotic behavior in nonlinear partial differential equations.
• Incompressible fluid mechanics: Navier-Stokes, Boussinesq, MHD systems, etc.
• Nonlinear dispersive wave equations (shallow water, Camassa--Holm, rod equations, etc.)
• Well-posedness and blowup issues
• Applications of harmonic analysis to PDEs

Habilitation à diriger des recherches (Dec. 8th, 2010. pdf file, 76 pages, in French).

Short english version of the habilitation (pdf file, 18 pages, 2010).

Book's chapter

Published or accepted papers

1. L. Brandolese, G. Karch Large self-similar solutions to Oberbeck--Boussinesq system with Newtonian gravitational field, J. Diff. Equ. 424 (2025), 139-158.


2. Y. Samoilenko, L. Brandolese, V. Samoilenko, Soliton-like solutions of the modified Camassa-Holm equation with variable coefficients, Chaos, Solitons and Fractals, 192, 2025, 115944. (pdf).


3. L. Brandolese, Ling-Yun Shou, Jiang Xu, Ping Zhang Sharp decay characterization of solutions to the compressible Navier-Stokes equations in the critical \(L^p\) framework, Adv. Math. 456, Article ID 109905, 60 p. (2024). (pdf).


4. L. Brandolese, C.F. Perusato, P.R. Zingano, On the topological size of the class of Leray solutions with algebraic decay, Bull. Lond. Math. Soc. 56, No. 1, 59-71 (2024). (pdf).
   
   
5. P. Biler, A. Boritchev, L. Brandolese, Sharp well-posedness and blowup results for parabolic systems of the Keller-Segel type Methods Appl. Anal. 30, No. 2, 53-76 (2024). (pdf).
   
   
6. P. Biler, A. Boritchev, L. Brandolese, Large global solutions of the parabolic-parabolic Keller-Segel system in higher dimensions J. Diff. Equ. 344 (2023) 891-914. (pdf).
   
   
7. L. Brandolese, T. Okabe, Forced rapidly dissipative Navier-Stokes flows, SIAM J. Math. Anal. 56, No. 1, 412-432 (2024). (pdf).


8. L. Brandolese, Hexagonal structures in 2D Navier-Stokes flows, Comm. PDE (https://doi.org/10.1080/03605302.2022.2037633), 2022. (pdf).


9. L. Brandolese, S. Monniaux, Well-posedness for the Boussinesq system in critical spaces via maximal regularity, Ann. Inst. Fourier 73 (2023) 1--20 (pdf).


10. L. Brandolese, Far field geometric structures of 2D flows with localised vorticity, Math. Annal. 383 no. 1-2, (2022) 699-714 . (pdf , published version)


11. L. Brandolese, T. Okabe, Annihilation of slowly-decaying terms of Navier-Stokes flows by external forcing, Nonlinearity, 34 no.3 (2021), 1733--1757. (HAL)


12. L. Brandolese, J. He, Uniqueness theorems for the Boussinesq system,
    Tohoku Math. J. (2) 72 no.2 (2020), 283--297. (pdf)


13. L. Brandolese, F. Cortez, Blowup for the nonlinear heat equation with small initial data in scale-invariant Besov norms,
    J. Funct. Anal. 276 (2019), 2589--2604. (pdf)


14. L. Brandolese, On a non-soleinoidal approximation to the incompressible Navier--Stokes equations,
    J. London Math. Soc. 96, N.2 (2017), 326--344. (pdf)


15. L. Brandolese, C. Mouzouni, A short proof of the large time energy growth for the Boussinesq system
    J. Nonlinear Sci. 27, N.5 (2017), 1589-1608. (pdf) (publisher file)


16. L. Brandolese, M.E. Schonbek, Large time behavior of Newtonian viscous incompressible fluids,
    Chapter 3.4 of the book (to appear): Handbook of Mathematical Analysis in Mechanics of Viscous Fluids.
    Springer. Yoshikazu Giga and Antonin Novotny editors. DOI 10.1007/978-3-319-10151-4_11-1. (pdf)


17. L. Brandolese, Characterization of solutions to dissipative systems with sharp algebraic decay,
    SIAM J. Math. Anal. 48, N. 3 (2016), 1616-1633. (pdf),
    


18. L. Brandolese, A Liouville Theorem for the Degasperis-Procesi Equation
    Ann. Scuola Norm. Sup. Pisa XVI, N. 3 (2016), 759--765 (pdf)


19. L. Brandolese, Manuel Fernando Cortez, On permanent and breaking waves in hyperelastic rods and rings
    J. Funct. Anal. 266 (2014), 6954-6987 (pdf)
    
 
20. L. Brandolese, Manuel Fernando Cortez, Blowup issues for a class of nonlinear dispersive wave equations
    J. Diff. Equ. 256 (2014) 3981-3998 (pdf)
    
 
21. L. Brandolese, Local-in-space criteria for blowup in shallow water and dispersive rod equations,
    Comm. Math. Phys., 330 (2014) 401--414 (pdf)
    
 
22. L. Brandolese, Breakdown for the Camassa--Holm equation using decay criteria and persistence in weighted spaces,
    Int. Math. Res. Not. rnr218 (2012), 5161--5181. (pdf)
     
23. L. Brandolese, M. E. Schonbek, Large time decay and growth for solutions of a viscous Boussinesq system,
    Trans. Amer. Math. Soc. 364 (2012) 5057-5090 (pdf)
 
24. C. Bjorland, L. Brandolese, D. Iftimie, M.E. Schonbek, L^p solutions of the stady-state Navier-Stokes equations with rough external forces,
    Comm. Part. Diff. Equ., 36 (2011), 216--246 (pdf)
 
25. H.-O. Bae, L. Brandolese, On the effect of external forces on the motion of incompressible flows at large distances
    Ann. Univ. Ferrara, VII Sci. 55 N.2, 225--238 (2009). (pdf)
 
26. P. Biler, L. Brandolese, On the Parabolic-elliptic limit of the doubly parabolic Keller--Segel system modelling chemotaxis,
    Studia Math., 193 N.3, 241--261 (2009). (pdf)
 
27. L. Brandolese, Concentration-diffusion effects in viscous incompressible flows,
    Indiana Univ. Math. J., 58, N.2, 789--806 (2009). (pdf)
 
28. H.-O. Bae, L. Brandolese, B. J. Jin,, Asymptotic behavior for the Navier--Stokes equations with nonzero external forces,
    Nonlinear analysis 71, N.12, e292-e302 (2009). Doi: 10.1016/j.na.2008.10.074 (pdf)
 
29. L. Brandolese, Fine properties of self-similar solutions of the Navier-Stokes equations
    Arch. Rational Mech. Anal., 192, N.3, 375--401 (2009) (pdf)
 
30. L. Brandolese, G. Karch, Far field asymptotics of solutions to convection equation with anomalous diffusion
    J. Evol. Equ. 8, 307--326 (2008) (pdf)
 
31. L. Brandolese, F. Vigneron , New asymptotic profiles of nonstationnary solutions of the Navier-Stokes system
    J. Math. Pures Appl. 88,64--86 (2007).   (pdf)
 
32. L. Brandolese, F. Vigneron , On the Localization of the magnetic and the velocity fields in the equations of magnetohydrodynamics ,
      Proc. Roy. Soc. Edinburgh 137A, 475--495 (2007). (pdf)
 
33. P. Biler, L. Brandolese, Global existence versus blow up for some models of interacting particles,
    Colloq. Math. 106, N.2, 293--303 (2006).   (pdf)
 
34. L. Brandolese, Application of  the realization of homogeneous Sobolev spaces to Navier-Stokes,
    SIAM J. Math. Anal. 37, N.2, 673-683 (2005)   (pdf)
 
35. L. Brandolese, Poisson kernels and sparse wavelet expansions,
    Proc. Amer. Math. Soc. 133, N. 11, 3345-3353 (2005) (pdf)
 
36. L. Brandolese, Weighted-L^2 spaces and strong solutions to the Navier-Stokes equations,
    Progr.  in Nonlinear Diff. Eq. and Appl. 61, 27-35 (2005)  
    
 
37. L. Brandolese, Space-time decay of Navier-Stokes flows invariant under rotations,
    Math. Ann. 329, 685-706 (2004)  (pdf)
 
38. L. Brandolese, Atomic decomposition for the vorticity of a viscous flow in the whole space,
    Math. Nachr. 273, 28-42 (2004)  (pdf)
 
39. L. Brandolese, Asymptotic behavior of the energy and pointwise estimates for solutions to the Navier-Stokes equations,
    Rev. Mat. Iberoamericana 20, 223-256 (2004) (pdf)
 
40. L. Brandolese, Localisation de la vorticité et applications au comportement asymptotique de Navier-Stokes,
    Journées Equations aux dérivées partielles, Forges-les-eaux, pp. III 1--13 (2002)
 
41. L. Brandolese, Y. Meyer, On the instantaneous spreading for the Navier-Stokes system in the whole space,
    Contr. Optim. Calc. Var. 8, pp. 273--285 (2002)  (pdf)
 
42. L. Brandolese, On the localization of symmetric and asymmetric solutions of the Navier--Stokes equations in R^n,
    C. R. Acad. Sci. Paris, Série I t. 332, pp. 125--130 (2001)

Ph.D dissertation