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The research of Paolo Secchi

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  • The research of Professor Paolo Secchi concerns the theory of partial differential equations, especially from fluid dynamics.

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  • [1]

    P. Secchi, On the initial value problem for the equation of motion of viscous incompressible fluids in the presence of diffusion, Boll. UMI B (6), 1 (1982), 1117-1130.

    [2]

    P. Secchi and A. Valli, A free boundary problem for compressible viscous fluids, J. Reine Angew. Math., 341 (1983), 1-31.doi: 10.1515/crll.1983.341.1.

    [3]

    P. Secchi, Existence theorems for compressible viscous fluids having zero shear viscosity, Rend. Sem. Mat. Univ. Padova, 71 (1984), 73-102.

    [4]

    V. Casulli, G. Pontrelli and P. Secchi, An Eulerian-Lagrangian method for open channel flows, in Numerical Methods in Laminar and Turbulent Flow, Part 1, 2 (Swansea, 1985), Pineridge, Swansea, 1985, 1360-1370.

    [5]

    P. Secchi, Flussi non stazionari di fluidi incompressibili viscosi e ideali in un semipiano, Ricerche di Matematica, 34 (1985), 27-44.

    [6]

    H. Beirão da Veiga and P. Secchi, $L^p$-stability for the strong solutions of the Navier-Stokes equations in the whole space, Arch. Rat. Mech. Anal., 98 (1987), 65-69.doi: 10.1007/BF00279962.

    [7]

    P. Secchi, $L^2$-stability for weak solutions of the Navier-Stokes equations in $\mathbbR^3$, Indiana Univ. Math. J., 36 (1987), 685-691.doi: 10.1512/iumj.1987.36.36039.

    [8]

    P. Marcati, A. J. Milani and P. Secchi, Singular convergence of weak solutions for a quasilinear nonhomogeneous hyperbolic system, Manuscripta Mathematica, 60 (1988), 49-69.doi: 10.1007/BF01168147.

    [9]

    P. Secchi, On the motion of viscous fluids in the presence of diffusion, SIAM J. on Math. Anal., 19 (1988), 22-31.doi: 10.1137/0519002.

    [10]

    P. Secchi, On the stationary and nonstationary Navier-Stokes equations in $\mathbbR^n$, Ann. Mat. Pura Appl. (IV), 153 (1988), 293-306.doi: 10.1007/BF01762396.

    [11]

    P. Secchi, A note on the generic solvability of the Navier-Stokes equations, Rend. Sem. Mat. Univ. Padova, 83 (1990), 177-182.

    [12]

    P. Secchi, On the motion of gaseous stars in the presence of radiation, Comm. P.D.E., 15 (1990), 185-204.doi: 10.1080/03605309908820683.

    [13]

    P. Secchi, On the uniqueness of motion of viscous gaseous stars, Math. Methods Appl. Sci., 13 (1990), 391-404.doi: 10.1002/mma.1670130504.

    [14]

    P. Secchi, On the evolution equations of viscous gaseous stars, Ann. Scuola Norm. Sup. Pisa, 18 (1991), 295-318.

    [15]

    P. Secchi, On nonviscous compressible fluids in a time-dependent domain, Ann. Inst. Henri Poincaré, Analyse non linéaire, 9 (1992), 683-704.

    [16]

    P. Secchi, On the motion of nonviscous compressible fluids in domains with boundary, Partial Differential Equations, Banach Center Publications, Warszawa, 27 (1992), 447-455.

    [17]

    P. Secchi, On the equations of ideal incompressible magneto-hydrodynamics, Rend. Sem. Mat. Univ. Padova, 90 (1993), 103-119.

    [18]

    P. Secchi, Mixed problems for linear symmetric hyperbolic systems with characteristic boundary condition, in Qualitative Aspects and Applications of Nonlinear Evolution Equations (Trieste, 1993), World Sci. Publ., River Edge, NJ, 1994, 88-98.

    [19]

    P. Secchi, On a stationary problem for the compressible Navier-Stokes equations, Differential Integral Equations, 7 (1994), 463-482.

    [20]

    P. Secchi, On the stationary motion of compressible viscous fluids, Ann. Scuola Norm. Sup. Pisa, 21 (1994), 131-143.

    [21]

    P. Secchi, Linear symmetric hyperbolic systems with characteristic boundary, Math. Methods Appl. Sci., 18 (1995), 855-870.doi: 10.1002/mma.1670181103.

    [22]

    P. Secchi, On an initial boundary value problem for the equations of ideal magneto-hydrodynamics, Math. Methods Appl. Sci., 18 (1995), 841-853.doi: 10.1002/mma.1670181102.

    [23]

    P. Secchi, On nonviscous compressible fluids in domains with moving boundaries, in Nonlinear Variational Problems and Partial Differential Equations (Isola d'Elba, 1990), Pitman Res. Notes Math. Ser., 320, Longman Sci. Tech., Harlow, 1995, 229-244.

    [24]

    P. Secchi, Well-posedness for a mixed problem for the equations of ideal magneto-hydrodynamics, Archiv Math. (Basel), 64 (1995), 237-245.doi: 10.1007/BF01188574.

    [25]

    P. Secchi, The initial boundary value problem for linear symmetric hyperbolic systems with characteristic boundary of constant multiplicity, Differential Integral Equations, 9 (1996), 671-700.

    [26]

    P. Secchi, Well-posedness of characteristic symmetric hyperbolic systems, Arch. Rat. Mech. Anal., 134 (1996), 155-197.doi: 10.1007/BF00379552.

    [27]

    P. Secchi, Characteristic symmetric hyperbolic systems with dissipation: Global existence and asymptotics, Math. Methods Appl. Sci., 20 (1997), 583-597.doi: 10.1002/(SICI)1099-1476(19970510)20:7<583::AID-MMA865>3.0.CO;2-T.

    [28]

    F. Gazzola and P. Secchi, Some results about stationary Navier-Stokes equations with a pressure-dependent viscosity, in Navier-Stokes Equations: Theory and Numerical Methods (Varenna, 1997), Pitman Res. Notes Math. Ser., 388, Longman, Harlow, 1998, 31-37.

    [29]

    P. Secchi, Inflow-outflow problems for inviscid compressible fluids, Commun. Appl. Anal., 2 (1998), 81-110.

    [30]

    P. Secchi, The open boundary problem for inviscid compressible fluids, in Navier-Stokes Equations and Related Nonlinear Problems (Palanga, 1997), VSP, Utrecht, 1998, 279-300.

    [31]

    P. Secchi, A symmetric positive system with nonuniformly characteristic boundary, Differential Integral Equations, 11 (1998), 605-621.

    [32]

    P. Secchi, Full regularity of solutions to a nonuniformly characteristic boundary value problem for symmetric positive systems, Adv. Math. Sci. Appl., 10 (2000), 39-55.

    [33]

    P. Secchi, On the incompressible limit of inviscid compressible fluids, Ann. Univ. Ferrara Sez. VII (N.S.), 46 (2000), 21-33.

    [34]

    P. Secchi, On the singular incompressible limit of inviscid compressible fluids, J. Math. Fluid Mech., 2 (2000), 107-125.doi: 10.1007/PL00000948.

    [35]

    P. Secchi, Some properties of anisotropic sobolev spaces, Archiv Math. (Basel), 75 (2000), 207-216.doi: 10.1007/s000130050494.

    [36]

    F. Gazzola and P. Secchi, Inflow-outflow problems for euler equations in a rectangular domain, NoDEA, 8 (2001), 195-217.doi: 10.1007/PL00001445.

    [37]

    E. Casella, P. Secchi and P. Trebeschi, Global existence of 2D slightly compressible viscous magneto-fluid motion, Portugaliae Mathematica, 59 (2002), 67-89.

    [38]

    P. Secchi, An initial boundary value problem in ideal magneto-hydrodynamics, NoDEA, 9 (2002), 441-458.doi: 10.1007/PL00012608.

    [39]

    P. Secchi, Life span and global existence of 2-D compressible fluids, in The Navier-Stokes Equations: Theory and Numerical Methods (Varenna, 2000), Lecture Notes in Pure and Appl. Math., 223, Dekker, New York, 2002, 99-111.

    [40]

    P. Secchi, Life span of 2-D irrotational compressible fluids in the halfplane, Math. Methods Appl. Sci., 25 (2002), 895-910.doi: 10.1002/mma.318.

    [41]

    P. Secchi, On slightly compressible ideal flow in the halfplane, Arch. Rat. Mech. Anal., 161 (2002), 231-255.doi: 10.1007/s002050100179.

    [42]

    P. Secchi, Pointwise decay for solutions of the 2D Neumann exterior problem for the wave equation II, Rend. Sem. Mat. Univ. Padova, 108 (2002), 67-77.

    [43]

    E. Casella, P. Secchi and P. Trebeschi, Global classical solutions of 2D MHD system, J. Math. Fluid Mech., 5 (2003), 70-91.doi: 10.1007/s000210300003.

    [44]

    P. Secchi and Y. Shibata, On the decay of solutions to the 2D Neumann exterior problem for the wave equation, J. Differential Equations, 194 (2003), 221-236.doi: 10.1016/S0022-0396(03)00189-X.

    [45]

    J.-F. Coulombel and P. Secchi, On the transition to instability for compressible vortex sheets, Proc. Roy. Soc. Edinburgh, 134 (2004), 885-892.doi: 10.1017/S0308210500003528.

    [46]

    J.-F. Coulombel and P. Secchi, The stability of compressible vortex sheets in two space dimensions, Indiana Univ. Math. J., 53 (2004), 941-1012.doi: 10.1512/iumj.2004.53.2526.

    [47]

    A. Morando and P. Secchi, On 3D slightly compressible Euler equations, Portugaliae Mathematica, 61 (2004), 301-316.

    [48]

    P. Secchi, Pointwise decay for solutions of the 2D Neumann exterior problem for the wave equation, Boll. UMI B (8), 7 (2004), 189-206.

    [49]

    J.-F. Coulombel and P. Secchi, Stability of compressible vortex sheets, in EQUADIFF 2003, World Sci. Publ., Hackensack, NJ, 2005, 502-504.doi: 10.1142/9789812702067_0081.

    [50]

    P. Secchi, On compressible vortex sheets, J. Math. Fluid Mech., 7 (2005), S254-S272.doi: 10.1007/s00021-005-0158-6.

    [51]

    P. Secchi and P. Trebeschi, Non-homogeneous quasi-linear symmetric hyperbolic systems with characteristic boundary, Int. J. Pure Appl. Math., 23 (2005), 39-59.

    [52]

    E. Casella, P. Secchi and P. Trebeschi, Non-homogeneous linear symmetric hyperbolic systems with characteristic boundary, Differential Integral Equations, 19 (2006), 51-74.

    [53]

    P. Secchi, 2D slightly compressible ideal flow in an exterior domain, J. Math. Fluid Mech., 8 (2006), 564-590.doi: 10.1007/s00021-005-0188-0.

    [54]

    P. Secchi, On compressible and incompressible vortex sheets, in Analysis and Simulation of Fluid Dynamics, Adv. Math. Fluid Mech., Birkhäuser, Basel, 2007, 201-228.doi: 10.1007/978-3-7643-7742-7_12.

    [55]

    J.-F. Coulombel and P. Secchi, Nonlinear compressible vortex sheets in two space dimensions, Ann. Sci. Éc. Norm. Supér. (4), 41 (2008), 85-139.

    [56]

    J.-F. Coulombel and P. Secchi, Nonlinear stability of compressible vortex sheets, in Hyperbolic Problems: Theory, Numerics, Applications, Springer, Berlin, 2008, 415-422.doi: 10.1007/978-3-540-75712-2_38.

    [57]

    J.-F. Coulombel and P. Secchi, Uniqueness of 2-D compressible vortex sheets, Comm. Pure Appl. Anal., 8 (2009), 1439-1450.doi: 10.3934/cpaa.2009.8.1439.

    [58]

    A. Morando, P. Secchi and P. Trebeschi, Characteristic initial boundary value problems for symmetrizable systems, Rend. Semin. Mat. Univ. Politec. Torino, 67 (2009), 229-245.

    [59]

    A. Morando, P. Secchi and P. Trebeschi, Regularity of solutions to characteristic initial-boundary value problems for symmetrizable systems, J. Hyperbolic Differ. Equ., 6 (2009), 753-808.doi: 10.1142/S021989160900199X.

    [60]

    P. Secchi, A. Morando and P. Trebeschi, Hyperbolic problems with characteristic boundary, in Qualitative Properties of Solutions to Partial Differential Equations, J. Nečas Cent. Math. Model. Lect. Notes, 5, Matfyzpress, Prague, 2009, 135-200.

    [61]

    D. Catania and P. Secchi, Global existence and finite dimensional global attractor for a 3D double viscous MHD-alpha model, Commun. Math. Sci., 8 (2010), 1021-1040.doi: 10.4310/CMS.2010.v8.n4.a12.

    [62]

    A. Morando and P. Secchi, Regularity of weakly well-posed characteristic boundary value problems, Int. J. Differ. Equ., (2010), Art. ID 524736, 39 pp.

    [63]

    P. Secchi, An alpha model for compressible fluids, Discrete Contin. Dyn. Syst. Ser. S, 3 (2010), 351-359.doi: 10.3934/dcdss.2010.3.351.

    [64]

    D. Catania and P. Secchi, Global existence for two regularized MHD models in three space-dimension, Portugaliae Mathematica, 68 (2011), 41-52.doi: 10.4171/PM/1880.

    [65]

    A. Morando and P. Secchi, Regularity of weakly well posed hyperbolic mixed problems with characteristic boundary, J. Hyperbolic Differ. Equ., 8 (2011), 37-99.doi: 10.1142/S021989161100238X.

    [66]

    D. Catania and P. Secchi, Global regularity for some MHD-alpha systems, Riv. Mat. Univ. Parma, 3 (2012), 25-39.

    [67]

    J.-F. Coulombel, A. Morando, P. Secchi and P. Trebeschi, A priori estimates for 3D incompressible current-vortex sheets, Commun. Math. Phys., 311 (2012), 247-275.doi: 10.1007/s00220-011-1340-8.

    [68]

    A. Morando and P. Secchi, Weakly well posed characteristic hyperbolic problems, Riv. Mat. Univ. Parma, 3 (2012), 147-162.

    [69]

    P. Secchi, A higher-order Hardy-type inequality in anisotropic Sobolev spaces, Int. J. Differ. Equ., (2012), Art. ID 129691, 7 pp.

    [70]

    P. Secchi and Y. Trakhinin, Well-posedness of the linearized plasma-vacuum interface problem, Interfaces and Free Boundaries, 15 (2013), 323-357.doi: 10.4171/IFB/305.

    [71]

    D. Catania, M. D'Abbicco and P. Secchi, Stability of the linearized MHD-Maxwell free interface problem, Comm. Pure Appl. Anal., 13 (2014), 2407-2443.doi: 10.3934/cpaa.2014.13.2407.

    [72]

    A. Morando, P. Secchi and P. Trebeschi, On a priori energy estimates for characteristic boundary value problems, J. Fourier Anal. Appl., 20 (2014), 816-864.doi: 10.1007/s00041-014-9335-4.

    [73]

    P. Secchi and Y. Trakhinin, Well-posedness of the plasma-vacuum interface problem, Nonlinearity, 27 (2014), 105-169.doi: 10.1088/0951-7715/27/1/105.

    [74]

    P. Secchi, Nonlinear surface waves on the plasma-vacuum interface, Quart. Appl. Math., to appear, 2015.doi: 10.1090/qam/1405.

    [75]

    P. Secchi, On the Nash-Moser iteration technique, in Recent Developments of Mathematical Fluid Mechanics, Adv. Math. Fluid Mech., Birkhäuser, Basel, to appear.

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