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The research of Paolo Secchi
Quantum hydrodynamics with nonlinear interactions
1. | Gran Sasso Science Institute, viale F. Crispi, 7, 67100 L'Aquila, Italy |
2. | DISIM - Università de L'Aquila, via Vetoio, 67010 Coppito (AQ), Italy |
References:
[1] |
P. Antonelli and P. Marcati, On the finite energy weak solutions to a system in quantum fluid dynamics,, Comm. Math. Phys., 287 (2009), 657.
doi: 10.1007/s00220-008-0632-0. |
[2] |
P. Antonelli and P. Marcati, The Quantum Hydrodynamics system in two space dimensions,, Archive for Rational Mechanics and Analysis, 203 (2012), 499.
doi: 10.1007/s00205-011-0454-7. |
[3] |
P. Antonelli, R. Carles and C. Sparber, On nonlinear Schrödinger type equations with nonlinear damping,, Int. Math. Res. Notices, 2015 (2015), 740.
doi: 10.1093/imrn/rnt217. |
[4] |
G. Baccarani and M. Wordeman, An investignation of steady state velocity overshoot effects in Si and GaAs devices,, Solid State Electron., ED-29 (1982), 970. Google Scholar |
[5] |
N. Berloff, Quantum vortices, travelling coherent structures and superfluid turbulence,, in Stationary and Time Dependent Gross-Pitaevskii Equations (eds. A. Farina and J.-C. Saut), (2006). Google Scholar |
[6] |
Y. Brenier, Polar factorization and monotone rearrangement of vector-valued function,, Comm. Pure Appl. Math., 44 (1991), 375.
doi: 10.1002/cpa.3160440402. |
[7] |
T. Cazenave, Semilinear Schödinger Equations,, Courant Lecture Notes in Mathematics, (2003).
|
[8] |
P. Constantin and J.-C. Saut, Local smoothing properties of dispsersive equations,, J. Amer. Math. Soc., 1 (1988), 413.
doi: 10.1090/S0894-0347-1988-0928265-0. |
[9] |
F. Dalfovo, S. Giorgini, L. Pitaevskii and S. Stringari, Theory of Bose-Einstein condensation in trapped gases,, Rev. Mod. Phys., 71 (1999), 463.
doi: 10.1103/RevModPhys.71.463. |
[10] |
D. Donatelli, E. Feireisl and P. Marcati, Well/ill posedness for the Euler-Korteweg-Poisson system and related problems,, Comm. PDEs, 40 (2015), 1314.
doi: 10.1080/03605302.2014.972517. |
[11] |
H. Federer and W. P. Ziemer, The Lebesgue set of a function whose distribution derivatives are $p^{th}$ power summable,, Indiana Univ. Math. J., 22 (1972), 139.
doi: 10.1512/iumj.1973.22.22013. |
[12] |
R. Feynman, Superfluidity and Superconductivity,, Rev. Mod. Phys., 29 (1957).
doi: 10.1103/RevModPhys.29.205. |
[13] |
C. Gardner, The quantum hydrodynamic model for semincoductor devices,, SIAM J. Appl. Math., 54 (1994), 409.
doi: 10.1137/S0036139992240425. |
[14] |
J. Ginibre and G. Velo, The global Cauchy problem for the nonlinear Schrödinger equations rivisited,, Ann. Inst. H. Poincaré Anal. Non Lin., 2 (1985), 309.
|
[15] |
A. Griffin, T. Nikuni and E. Zaremba, Bose-Condensed Gases at Finite Temperatures,, Cambridge University Press, (2009).
doi: 10.1017/CBO9780511575150. |
[16] |
A. Jüngel, Dissipative quantum fluid models,, Riv. Mat. Univ. Parma, 3 (2012), 217.
|
[17] |
A. Jüngel, M. Mariani and D. Rial, Local existence of solutions to the transient quantum hydrodynamics equations,, Math. Models Methods Appl. Sci., 12 (2002), 485.
doi: 10.1142/S0218202502001751. |
[18] |
M. Keel and T. Tao, Enpoint Strichartz estimates,, Amer. J. Math., 120 (1998), 955.
doi: 10.1353/ajm.1998.0039. |
[19] |
M. Kostin, On the Schrödinger-Langevin equation,, J. Chem. Phys., 57 (1972), 3589. Google Scholar |
[20] |
L. Landau, Theory of the superfluidity of helium II,, Phys. Rev., 60 (1941). Google Scholar |
[21] |
H. L. Li and P. Marcati, Existence and asymptotic behavior of multi-dimensional quanntum hydrodynamic model for semiconductors,, Comm. Math. Phys., 245 (2004), 215.
doi: 10.1007/s00220-003-1001-7. |
[22] |
F. Linares and G. Ponce, Introduction to Nonlinear Dispersive Equations,, Springer-Verlag, (2009).
|
[23] |
E. Madelung, Quantuentheorie in hydrodynamischer form,, Z. Physik, 40 (1927). Google Scholar |
[24] |
P. Marcati, P. Markowich and R. Natalini, Mathematical Problems in Semiconductor Physics,, Pitman Res. Notices in Math. Series, (1996). Google Scholar |
[25] |
P. Markowich, C. Ringhofer and C. Schmeiser, Semiconductor Equations,, Springer-Verlag, (1990).
doi: 10.1007/978-3-7091-6961-2. |
[26] |
J. M. Rakotoson and R. Temam, An optimal compactness theorem and application to elliptic-parabolic systems,, Appl. Math. Letters, 14 (2001), 303.
doi: 10.1016/S0893-9659(00)00153-1. |
[27] |
T. Tao, Nonlinear Dispersive Equations: Local and Global Analysis,, CBMS Regional Conference Series in Mathematics, (2006).
|
[28] |
M. Tsubota, Quantized vortices in superfluid helium and Bose-Einstein condensates,, J. Phys.: Conf. Ser., 31 (2006), 88.
doi: 10.1088/1742-6596/31/1/014. |
[29] |
E. Zaremba, T. Nikuni and A. Griffin, Dynamics of trapped Bose gases at finite temperatures,, J. Low Temp. Phys., 116 (1999), 277. Google Scholar |
show all references
References:
[1] |
P. Antonelli and P. Marcati, On the finite energy weak solutions to a system in quantum fluid dynamics,, Comm. Math. Phys., 287 (2009), 657.
doi: 10.1007/s00220-008-0632-0. |
[2] |
P. Antonelli and P. Marcati, The Quantum Hydrodynamics system in two space dimensions,, Archive for Rational Mechanics and Analysis, 203 (2012), 499.
doi: 10.1007/s00205-011-0454-7. |
[3] |
P. Antonelli, R. Carles and C. Sparber, On nonlinear Schrödinger type equations with nonlinear damping,, Int. Math. Res. Notices, 2015 (2015), 740.
doi: 10.1093/imrn/rnt217. |
[4] |
G. Baccarani and M. Wordeman, An investignation of steady state velocity overshoot effects in Si and GaAs devices,, Solid State Electron., ED-29 (1982), 970. Google Scholar |
[5] |
N. Berloff, Quantum vortices, travelling coherent structures and superfluid turbulence,, in Stationary and Time Dependent Gross-Pitaevskii Equations (eds. A. Farina and J.-C. Saut), (2006). Google Scholar |
[6] |
Y. Brenier, Polar factorization and monotone rearrangement of vector-valued function,, Comm. Pure Appl. Math., 44 (1991), 375.
doi: 10.1002/cpa.3160440402. |
[7] |
T. Cazenave, Semilinear Schödinger Equations,, Courant Lecture Notes in Mathematics, (2003).
|
[8] |
P. Constantin and J.-C. Saut, Local smoothing properties of dispsersive equations,, J. Amer. Math. Soc., 1 (1988), 413.
doi: 10.1090/S0894-0347-1988-0928265-0. |
[9] |
F. Dalfovo, S. Giorgini, L. Pitaevskii and S. Stringari, Theory of Bose-Einstein condensation in trapped gases,, Rev. Mod. Phys., 71 (1999), 463.
doi: 10.1103/RevModPhys.71.463. |
[10] |
D. Donatelli, E. Feireisl and P. Marcati, Well/ill posedness for the Euler-Korteweg-Poisson system and related problems,, Comm. PDEs, 40 (2015), 1314.
doi: 10.1080/03605302.2014.972517. |
[11] |
H. Federer and W. P. Ziemer, The Lebesgue set of a function whose distribution derivatives are $p^{th}$ power summable,, Indiana Univ. Math. J., 22 (1972), 139.
doi: 10.1512/iumj.1973.22.22013. |
[12] |
R. Feynman, Superfluidity and Superconductivity,, Rev. Mod. Phys., 29 (1957).
doi: 10.1103/RevModPhys.29.205. |
[13] |
C. Gardner, The quantum hydrodynamic model for semincoductor devices,, SIAM J. Appl. Math., 54 (1994), 409.
doi: 10.1137/S0036139992240425. |
[14] |
J. Ginibre and G. Velo, The global Cauchy problem for the nonlinear Schrödinger equations rivisited,, Ann. Inst. H. Poincaré Anal. Non Lin., 2 (1985), 309.
|
[15] |
A. Griffin, T. Nikuni and E. Zaremba, Bose-Condensed Gases at Finite Temperatures,, Cambridge University Press, (2009).
doi: 10.1017/CBO9780511575150. |
[16] |
A. Jüngel, Dissipative quantum fluid models,, Riv. Mat. Univ. Parma, 3 (2012), 217.
|
[17] |
A. Jüngel, M. Mariani and D. Rial, Local existence of solutions to the transient quantum hydrodynamics equations,, Math. Models Methods Appl. Sci., 12 (2002), 485.
doi: 10.1142/S0218202502001751. |
[18] |
M. Keel and T. Tao, Enpoint Strichartz estimates,, Amer. J. Math., 120 (1998), 955.
doi: 10.1353/ajm.1998.0039. |
[19] |
M. Kostin, On the Schrödinger-Langevin equation,, J. Chem. Phys., 57 (1972), 3589. Google Scholar |
[20] |
L. Landau, Theory of the superfluidity of helium II,, Phys. Rev., 60 (1941). Google Scholar |
[21] |
H. L. Li and P. Marcati, Existence and asymptotic behavior of multi-dimensional quanntum hydrodynamic model for semiconductors,, Comm. Math. Phys., 245 (2004), 215.
doi: 10.1007/s00220-003-1001-7. |
[22] |
F. Linares and G. Ponce, Introduction to Nonlinear Dispersive Equations,, Springer-Verlag, (2009).
|
[23] |
E. Madelung, Quantuentheorie in hydrodynamischer form,, Z. Physik, 40 (1927). Google Scholar |
[24] |
P. Marcati, P. Markowich and R. Natalini, Mathematical Problems in Semiconductor Physics,, Pitman Res. Notices in Math. Series, (1996). Google Scholar |
[25] |
P. Markowich, C. Ringhofer and C. Schmeiser, Semiconductor Equations,, Springer-Verlag, (1990).
doi: 10.1007/978-3-7091-6961-2. |
[26] |
J. M. Rakotoson and R. Temam, An optimal compactness theorem and application to elliptic-parabolic systems,, Appl. Math. Letters, 14 (2001), 303.
doi: 10.1016/S0893-9659(00)00153-1. |
[27] |
T. Tao, Nonlinear Dispersive Equations: Local and Global Analysis,, CBMS Regional Conference Series in Mathematics, (2006).
|
[28] |
M. Tsubota, Quantized vortices in superfluid helium and Bose-Einstein condensates,, J. Phys.: Conf. Ser., 31 (2006), 88.
doi: 10.1088/1742-6596/31/1/014. |
[29] |
E. Zaremba, T. Nikuni and A. Griffin, Dynamics of trapped Bose gases at finite temperatures,, J. Low Temp. Phys., 116 (1999), 277. Google Scholar |
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