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Equazioni alle derivate parziali della fisica matematica

 

PERSONE

Hugo Beirão da Veiga
Luigi Carlo Berselli
Francesca Crispo
Carlo Romano Grisanti

LINEE GENERALI DI ATTIVITA'

Metodi Analitici e Numerici nello studio delle Equazioni alle Derivate Parziali con particolare riguardo alla Meccanica dei Fluidi.

OBIETTIVI FONDAMENTALI

Studio teorico e numerico dei sistemi di equazioni non-lineari della meccanica dei fluidi. In particolare si studiano le equazioni di Eulero e Navier-Stokes, e alcune delle loro generalizzazioni di notevole importanza nelle applicazioni.

PUBBLICAZIONI RECENTI

  • H. Beirao da Veiga, Navier-Stokes equations with shear thickening viscosity. Regularity up to the boundary, J. Math. Fluid Mechanics, vol.9 (2007) .
  • H. Beirao da Veiga, Navier-Stokes equations with shear thinning viscosity. Regularity up to the boundary,  J. Math. Fluid Mechanics, in press.
  • H. Beirao da Veiga, On the Ladyzhenskaya-Smagorinsky turbulence model of the Navier-Stokes equations. Regularity up to the boundary, J.Europ.  Math. Soc., in press.
  • H. Beirao da Veiga, Remarks on the Navier-Stokes equations under slip type boundary conditions with linear friction, Portugaliae Math., vol.64 (2008).
  • H. Beirao da Veiga, On the regularity of flows with Ladyzhenskaya shear dependent viscosity and slip and non-slip boundary conditions, Comm. Pure Appl. Math., vol. 58, (2005), pp. 552-577.
  • H. Beirao da Veiga, Vorticity and regularity for viscous incompressible flows under the Dirichlet boundary condition. Results and related open problems, J. Math. Fluid Mechanics, vol.8 (2006), 1-11.
  • H. Beirao da Veiga, On time-periodic solutions of the Navier-Stokes equations in unbounded cylindrical domains. Leray's problem for periodic flows. Arch. Rat. Mech. Analysis, vol. 178, pp. 301-325.
  • H. Beirao da Veiga, Regularity of solutions to a non homogeneous boundary value problem for general Stokes systems in R^n, Math. Annalen. vol. 331, pp. 203-217.
  • H. Beirao da Veiga, Developable surfaces as generators of the isobaric solutions to the Euler equations. J. Math. Fluid Mechanics. vol. 6, pp. 430-438.
  • H. Beirao da Veiga, On the existence of strong solutions to a coupled fluid-structure evolution problem. J. Math. Fluid Mechanics. vol. 6, pp. 21-52.
  • H. Beirao da Veiga, Regularity for Stokes and generalized Stokes systems under non homogeneous slip type boundary conditions. Advances Diff. Eq., Vol. 9, pp. 1079-1114.
  • H. Beirao da Veiga, Concerning time-periodic solutions of the Navier-Stokes equations in cylindrical domains under Navier boundary conditions, J. Partial Diff. Eq., vol.19 (2006), 1-11.
  • H. Beirao da Veiga, Vorticity and regularity for flows under the Navier boundary condition, Comm. Pure Applied Analysis, vol.5 (2006), 907-918.
  • L.C. Berselli, On the W^{2,q}-regularity of incompressible fluids with shear-dependent viscosities: The shear thinning case, J. Math. Fluid Mech, in press.
  • L.C. Berselli and M. Gubinelli, On the global evolution of vortex filaments, blobs, and small loops in 3D ideal flows, Comm. Math. Phys. 269 (2007), 693--713.
  • L.C. Berselli, T. Iliescu, and W.J. Layton Mathematics of Large Eddy Simulation of Turbulent Flows, pp. xviii+348,(2005), ISBN 3-540-26316-0 Springer series in Scientific Computation.
  • L.C. Berselli and M. Romito, On the existence and uniqueness of weak solutions for a vorticity seeding model, SIAM J. Math. Anal. 37 (2006), 1780--1799.
  • L.C. Berselli and V. John, Asymptotic behavior of commutation errors and the divergence of the Reynolds stress tensor near the wall in the turbulent channel flow, Math. Meth. Appl. Sci., 29 (2006) 1709-1719.
  • L.C. Berselli, On the Large Eddy Simulation of the Taylor-Green vortex, J. Math. Fluid Mech. 7 (2005) S164--S191.
  • L.C. Berselli and G.P.~Galdi, On the space-time regularity of C(0,T;L^n)-very weak solutions to the Navier-Stokes equations, Nonlinear Anal. 58 (2004), 703--717.
  • L.C. Berselli and R. Manfrin, On a theorem by Sohr for the Navier-Stokes equations, J. Evol. Equ 4 (2004), 193--211.
  • L.C. Berselli and Paolo Guasoni, \emph{Some problems of shape optimization arising in stationary fluid motion, Adv. Math. Sci. Appl., 12 (2004) 279-293.
  • L.C. Berselli and T. Iliescu, A Higher Order Subfilter-Scale Model for Large Eddy Simulation, J. Comput. Appl.  Math. 159 (2003) 411-430.
  • L.C. Berselli, Vanishing viscosity limit and long-time behavior for 2D quasi-geostrophic equations, Indiana Univ.  Math. J. 51 (2002) 905--930.
  • L.C. Berselli and H.Bessaih, Some results for the line vortex equation, Nonlinearity 15 (2002)  1729--1746.
  • F. Crispo, P. Maremonti, Navier-Stokes equations in aperture domains: global existence with bounded flux and time-periodic solutions, Math. Meth. Appl. Sci. To appear
  • F. Crispo, Shear thinning viscous fluids in cylindrical domains. Regularity up to the boundary, J. Math. Fluid Mech.,  To Appear.
  • F. Crispo, Global Regularity of a Class of p-Fluid Flows in Cylinders, Journal of Mathematical Analysis and Applications. To appear.
  • F. Crispo, A. Tartaglione, On the asymptotic stability of steady solutions of the Navier-Stokes equations in unbounded domains,  Math. Meth. Appl. Sci., 30 (2007), 1375--1401.
  • F. Crispo, P. Maremonti, An interpolation inequality in exterior domains, Rendiconti del Seminario Matematico di Padova, 112 (2004), 11--39.
  • F. Crispo, P. Maremonti, On the (x,t) asymptotic properties of solutions of the Navier-Stokes equations in the half-space, Zap. Nauc. Seminar POMI, 318 (2004), 147--202;  Journal of Math. Sci. N.Y., 136 (2006), 3735--3767.
  • F. Crispo, On the regularity of shear thickening viscous fluids, in press.
  • H. Beirao da Veiga and L.C. Berselli, Navier-Stokes equations: Green's matrices, vorticity direction and regularity up to the boundary, J. Diff. Eq., in press.
  • H. Beirao da Veiga and L.C. Berselli, On the regularizing effect of the vorticity direction in incompressible viscous flows, Differential Integral Equations 15 (2002), 345--356.
  • L.C. Berselli, C.R. Grisanti, and Volker John, Analysis of commutation errors for functions with low regularity, J. Comput. Appl.  Math. 206 (2007), 1027--1045.
  • D. Barbato, L.C. Berselli, and C.R. Grisanti, Analytical and numerical results for the Rational Large Eddy Simulation model, J. Math.  Fluid Mech. 9 (2007), 44--74.
  • L.C. Berselli and Carlo R. Grisanti, On the consistency of the Rational Large Eddy Simulation model, Comput.  Vis. Sci. 6 (2004), 75--82.
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