- Previous Article
- DCDS Home
- This Issue
-
Next Article
Note on the blowup criterion of smooth solution to the incompressible viscoelastic flow
Existence of multidimensional non-isothermal phase transitions in a steady van der Waals flow
1. | Business information management school, Shanghai institute of foreign trade, 1900 Wenxiang Rd., Shanghai 201620, China |
References:
[1] |
S. Alinhac, Existence d'ondes de raréfaction pour des systèmes quasi-linéaires hyperboliques multidimensionnels, Comm. Partial Differential Equaitons, 14 (1989), 173-230.
doi: 10.1080/03605308908820595. |
[2] |
N. Bedjaoui and P. G. LeFloch, Diffusive-dispersive traveling waves and kinetic relations, Proc. Royal Soc. Edinburgh, 132 (2002), 545-565.
doi: 10.1017/S0308210500001773. |
[3] |
S. Benzoni-Gavage, Nonuniqueness of phase transitions near the Maxwell line, Proc. Amer. Math. Soc., 127 (1999), 1183-1190.
doi: 10.1090/S0002-9939-99-04719-X. |
[4] |
S. Benzoni-Gavage, Stability of multi-dimensional phase transitions in a van der Waals fluid, Nonlinear Analysis, T.M.A., 31 (1998), 243-263.
doi: 10.1016/S0362-546X(96)00309-4. |
[5] |
S. Benzoni-Gavage, Stability of subsonic planar phase boundaries in a van der Waals fluid, Arch. Rational Mech. Anal., 150 (1999), 23-55.
doi: 10.1007/s002050050179. |
[6] |
S. Chen, Global existence of supersonic flow past a curved convex wedge, J. Partial Differential Equation, 11 (1998), 43-62. |
[7] |
R. Courant and K. O. Friedrichs, "Supersonic Flow and Shock Waves," Springer-Verlag, New York, 1977. |
[8] |
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. |
[9] |
J. F. Coulombel and P. Secchi, Nonlinear compressible vortex sheets in two space dimensions,, Preprint., ().
|
[10] |
H. Fan and M. Slemrod, Dynamic flows with liquid/vapor phase transitions, in "Handbook of Mathematical Fluid Dynamics" North-Holland, Amsterdam, (2002), 373-420.
doi: 10.1016/S1874-5792(02)80011-8. |
[11] |
M. Grinfeld, Nonisothermal dynamic phase transitions, Quarterly Appl. Math., 47 (1989), 71-84. |
[12] |
H. Hattori, The Riemann problem for a van der Waals fluid with entropy rate admissibility criterion nonisothermal case, J. Differential Equation, 65 (1986), 158-174.
doi: 10.1016/0022-0396(86)90031-8. |
[13] |
H. O. Kreiss, Initial boundary value problems for hyperbolic systems, Comm. Pure Appl. Math., 23 (1970), 227-298. |
[14] |
D. J. Korteweg, Sur la forme que prennent leéquation des fluides si l'on tient compte des forces capilaires par des variantions densité, Arch. Néer. Sci. Exactes Sér., 2 (1901), 1-24. |
[15] |
P. D. Lax, Hyperbolic systems of conservation laws. II, Comm. Pure Appl. Math., 10 (1957), 537-467. |
[16] |
P. G. LeFloch, Propagating phase boundaries: formulation of the problem and existence via the Glimm method, Arch. Rational Mech. Anal., 123 (1993), 153-197.
doi: 10.1007/BF00695275. |
[17] |
P. G. LeFloch, "Hyperbolic Systems of Conservation Laws. The Theory of Classical and Nonclassical Shock Waves," ETH Lectures in Mathematics, Birkhauser, 2002.
doi: 10.1007/978-3-0348-8150-0. |
[18] |
W. Lien and T. P. Liu, Nonlinear stability of a self-similar 3-dimensional gas flow, Commun. Math. Phys., 204 (1999), 525-549.
doi: 10.1007/s002200050656. |
[19] |
A. Majda, The stability of multi-dimensional shock fronts, Mem. Amer. Math. Soc., 275 (1983), 1-95. |
[20] |
A. Majda, The existence of multi-dimensional shock fronts, Mem. Amer. Math. Soc., 281 (1983), 1-93. |
[21] |
G. Métivier, Stability of multimensional shock fronts, in "Advances in The Theory of Shock Waves" 47 PnDEA, Birkhäuser, Boston, (2001), 25-103. |
[22] |
C. S. Morawetz, On a weak solution for transonic flow problem, Comm. Pure Appl. Math., 38 (1985), 423-443.
doi: 10.1002/cpa.3160380610. |
[23] |
M. Shearer, Nonuniqueness of admissible solutions of Riemann initial value problem for a system of conservation laws of mixed type, Arch. Rational Mech. Anal., 93 (1986), 45-49.
doi: 10.1007/BF00250844. |
[24] |
M. Slemrod, Admissibility criteria for propagating phase boundaries in a van der Waals fluid, Arch. Rational Mech. Anal., 81 (1983), 301-315.
doi: 10.1007/BF00250857. |
[25] |
M. Slemrod, Dynamic phase transitions in a van der waals fluid, J. Differential Equations, 52 (1984), 1-23.
doi: 10.1016/0022-0396(84)90130-X. |
[26] |
Y.-G. Wang and Z. Xin, Stability and existence of multidimensional subsonic phase transitions, Acta Math. Appl. Sinica, 19 (2003), 529-558.
doi: 10.1007/210255-003-0130-2. |
[27] |
S.-Y. Zhang, Existence of travelling waves in non-isothermal phase dynamics, J. Hyperbolic Differential Equations, 4 (2007), 391-400.
doi: 10.1142/S0219891607001197. |
[28] |
S.-Y. Zhang, Stability of non-isothermal phase transitions in a steady van der waals flow,, Preprint., ().
|
[29] |
S.-Y. Zhang, Discontinuous solutions to the Euler equations in a van der Waals fluid, Appl. Math. Letters, 20 (2007), 170-176.
doi: 10.1016/j.aml.2006.03.010. |
[30] |
Y. Zhang, Global existence of steady supersonic potential flow past a curved wedge with a piecewise smooth boundary, SIAM J. Math. Anal., 31 (1999), 166-183.
doi: 10.1137/S0036141097331056. |
show all references
References:
[1] |
S. Alinhac, Existence d'ondes de raréfaction pour des systèmes quasi-linéaires hyperboliques multidimensionnels, Comm. Partial Differential Equaitons, 14 (1989), 173-230.
doi: 10.1080/03605308908820595. |
[2] |
N. Bedjaoui and P. G. LeFloch, Diffusive-dispersive traveling waves and kinetic relations, Proc. Royal Soc. Edinburgh, 132 (2002), 545-565.
doi: 10.1017/S0308210500001773. |
[3] |
S. Benzoni-Gavage, Nonuniqueness of phase transitions near the Maxwell line, Proc. Amer. Math. Soc., 127 (1999), 1183-1190.
doi: 10.1090/S0002-9939-99-04719-X. |
[4] |
S. Benzoni-Gavage, Stability of multi-dimensional phase transitions in a van der Waals fluid, Nonlinear Analysis, T.M.A., 31 (1998), 243-263.
doi: 10.1016/S0362-546X(96)00309-4. |
[5] |
S. Benzoni-Gavage, Stability of subsonic planar phase boundaries in a van der Waals fluid, Arch. Rational Mech. Anal., 150 (1999), 23-55.
doi: 10.1007/s002050050179. |
[6] |
S. Chen, Global existence of supersonic flow past a curved convex wedge, J. Partial Differential Equation, 11 (1998), 43-62. |
[7] |
R. Courant and K. O. Friedrichs, "Supersonic Flow and Shock Waves," Springer-Verlag, New York, 1977. |
[8] |
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. |
[9] |
J. F. Coulombel and P. Secchi, Nonlinear compressible vortex sheets in two space dimensions,, Preprint., ().
|
[10] |
H. Fan and M. Slemrod, Dynamic flows with liquid/vapor phase transitions, in "Handbook of Mathematical Fluid Dynamics" North-Holland, Amsterdam, (2002), 373-420.
doi: 10.1016/S1874-5792(02)80011-8. |
[11] |
M. Grinfeld, Nonisothermal dynamic phase transitions, Quarterly Appl. Math., 47 (1989), 71-84. |
[12] |
H. Hattori, The Riemann problem for a van der Waals fluid with entropy rate admissibility criterion nonisothermal case, J. Differential Equation, 65 (1986), 158-174.
doi: 10.1016/0022-0396(86)90031-8. |
[13] |
H. O. Kreiss, Initial boundary value problems for hyperbolic systems, Comm. Pure Appl. Math., 23 (1970), 227-298. |
[14] |
D. J. Korteweg, Sur la forme que prennent leéquation des fluides si l'on tient compte des forces capilaires par des variantions densité, Arch. Néer. Sci. Exactes Sér., 2 (1901), 1-24. |
[15] |
P. D. Lax, Hyperbolic systems of conservation laws. II, Comm. Pure Appl. Math., 10 (1957), 537-467. |
[16] |
P. G. LeFloch, Propagating phase boundaries: formulation of the problem and existence via the Glimm method, Arch. Rational Mech. Anal., 123 (1993), 153-197.
doi: 10.1007/BF00695275. |
[17] |
P. G. LeFloch, "Hyperbolic Systems of Conservation Laws. The Theory of Classical and Nonclassical Shock Waves," ETH Lectures in Mathematics, Birkhauser, 2002.
doi: 10.1007/978-3-0348-8150-0. |
[18] |
W. Lien and T. P. Liu, Nonlinear stability of a self-similar 3-dimensional gas flow, Commun. Math. Phys., 204 (1999), 525-549.
doi: 10.1007/s002200050656. |
[19] |
A. Majda, The stability of multi-dimensional shock fronts, Mem. Amer. Math. Soc., 275 (1983), 1-95. |
[20] |
A. Majda, The existence of multi-dimensional shock fronts, Mem. Amer. Math. Soc., 281 (1983), 1-93. |
[21] |
G. Métivier, Stability of multimensional shock fronts, in "Advances in The Theory of Shock Waves" 47 PnDEA, Birkhäuser, Boston, (2001), 25-103. |
[22] |
C. S. Morawetz, On a weak solution for transonic flow problem, Comm. Pure Appl. Math., 38 (1985), 423-443.
doi: 10.1002/cpa.3160380610. |
[23] |
M. Shearer, Nonuniqueness of admissible solutions of Riemann initial value problem for a system of conservation laws of mixed type, Arch. Rational Mech. Anal., 93 (1986), 45-49.
doi: 10.1007/BF00250844. |
[24] |
M. Slemrod, Admissibility criteria for propagating phase boundaries in a van der Waals fluid, Arch. Rational Mech. Anal., 81 (1983), 301-315.
doi: 10.1007/BF00250857. |
[25] |
M. Slemrod, Dynamic phase transitions in a van der waals fluid, J. Differential Equations, 52 (1984), 1-23.
doi: 10.1016/0022-0396(84)90130-X. |
[26] |
Y.-G. Wang and Z. Xin, Stability and existence of multidimensional subsonic phase transitions, Acta Math. Appl. Sinica, 19 (2003), 529-558.
doi: 10.1007/210255-003-0130-2. |
[27] |
S.-Y. Zhang, Existence of travelling waves in non-isothermal phase dynamics, J. Hyperbolic Differential Equations, 4 (2007), 391-400.
doi: 10.1142/S0219891607001197. |
[28] |
S.-Y. Zhang, Stability of non-isothermal phase transitions in a steady van der waals flow,, Preprint., ().
|
[29] |
S.-Y. Zhang, Discontinuous solutions to the Euler equations in a van der Waals fluid, Appl. Math. Letters, 20 (2007), 170-176.
doi: 10.1016/j.aml.2006.03.010. |
[30] |
Y. Zhang, Global existence of steady supersonic potential flow past a curved wedge with a piecewise smooth boundary, SIAM J. Math. Anal., 31 (1999), 166-183.
doi: 10.1137/S0036141097331056. |
[1] |
Myoungjean Bae, Hyangdong Park. Three-dimensional supersonic flows of Euler-Poisson system for potential flow. Communications on Pure and Applied Analysis, 2021, 20 (7&8) : 2421-2440. doi: 10.3934/cpaa.2021079 |
[2] |
Martin Gugat, Michael Herty, Siegfried Müller. Coupling conditions for the transition from supersonic to subsonic fluid states. Networks and Heterogeneous Media, 2017, 12 (3) : 371-380. doi: 10.3934/nhm.2017016 |
[3] |
Jan Prüss, Yoshihiro Shibata, Senjo Shimizu, Gieri Simonett. On well-posedness of incompressible two-phase flows with phase transitions: The case of equal densities. Evolution Equations and Control Theory, 2012, 1 (1) : 171-194. doi: 10.3934/eect.2012.1.171 |
[4] |
Yanbo Hu, Tong Li. Sonic-supersonic solutions for the two-dimensional pseudo-steady full Euler equations. Kinetic and Related Models, 2019, 12 (6) : 1197-1228. doi: 10.3934/krm.2019046 |
[5] |
José Luiz Boldrini, Luís H. de Miranda, Gabriela Planas. On singular Navier-Stokes equations and irreversible phase transitions. Communications on Pure and Applied Analysis, 2012, 11 (5) : 2055-2078. doi: 10.3934/cpaa.2012.11.2055 |
[6] |
Honghu Liu. Phase transitions of a phase field model. Discrete and Continuous Dynamical Systems - B, 2011, 16 (3) : 883-894. doi: 10.3934/dcdsb.2011.16.883 |
[7] |
Shaoqiang Tang, Huijiang Zhao. Stability of Suliciu model for phase transitions. Communications on Pure and Applied Analysis, 2004, 3 (4) : 545-556. doi: 10.3934/cpaa.2004.3.545 |
[8] |
Tatyana S. Turova. Structural phase transitions in neural networks. Mathematical Biosciences & Engineering, 2014, 11 (1) : 139-148. doi: 10.3934/mbe.2014.11.139 |
[9] |
Gui-Qiang Chen, Jun Chen, Mikhail Feldman. Transonic flows with shocks past curved wedges for the full Euler equations. Discrete and Continuous Dynamical Systems, 2016, 36 (8) : 4179-4211. doi: 10.3934/dcds.2016.36.4179 |
[10] |
Holger Dullin, Yuri Latushkin, Robert Marangell, Shibi Vasudevan, Joachim Worthington. Instability of unidirectional flows for the 2D α-Euler equations. Communications on Pure and Applied Analysis, 2020, 19 (4) : 2051-2079. doi: 10.3934/cpaa.2020091 |
[11] |
Irena Lasiecka, Justin Webster. Eliminating flutter for clamped von Karman plates immersed in subsonic flows. Communications on Pure and Applied Analysis, 2014, 13 (5) : 1935-1969. doi: 10.3934/cpaa.2014.13.1935 |
[12] |
Eun Heui Kim. Boundary gradient estimates for subsonic solutions of compressible transonic potential flows. Conference Publications, 2007, 2007 (Special) : 573-579. doi: 10.3934/proc.2007.2007.573 |
[13] |
Li Liu. Unique subsonic compressible potential flows in three -dimensional ducts. Discrete and Continuous Dynamical Systems, 2010, 27 (1) : 357-368. doi: 10.3934/dcds.2010.27.357 |
[14] |
Guanming Gai, Yuanyuan Nie, Chunpeng Wang. A degenerate elliptic problem from subsonic-sonic flows in convergent nozzles. Communications on Pure and Applied Analysis, 2021, 20 (7&8) : 2555-2577. doi: 10.3934/cpaa.2021070 |
[15] |
Yanbo Hu, Jiequan Li. On a supersonic-sonic patch arising from the frankl problem in transonic flows. Communications on Pure and Applied Analysis, 2021, 20 (7&8) : 2643-2663. doi: 10.3934/cpaa.2021015 |
[16] |
Steffen Arnrich. Modelling phase transitions via Young measures. Discrete and Continuous Dynamical Systems - S, 2012, 5 (1) : 29-48. doi: 10.3934/dcdss.2012.5.29 |
[17] |
Paola Goatin. Traffic flow models with phase transitions on road networks. Networks and Heterogeneous Media, 2009, 4 (2) : 287-301. doi: 10.3934/nhm.2009.4.287 |
[18] |
Pavel Drábek, Stephen Robinson. Continua of local minimizers in a quasilinear model of phase transitions. Discrete and Continuous Dynamical Systems, 2013, 33 (1) : 163-172. doi: 10.3934/dcds.2013.33.163 |
[19] |
Mauro Fabrizio, Claudio Giorgi, Angelo Morro. Isotropic-nematic phase transitions in liquid crystals. Discrete and Continuous Dynamical Systems - S, 2011, 4 (3) : 565-579. doi: 10.3934/dcdss.2011.4.565 |
[20] |
Nicolai T. A. Haydn. Phase transitions in one-dimensional subshifts. Discrete and Continuous Dynamical Systems, 2013, 33 (5) : 1965-1973. doi: 10.3934/dcds.2013.33.1965 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]