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Remarks on the free boundary problem of compressible Euler equations in physical vacuum with general initial densities
1. | Institute of Mathematics, Academy of Mathematics and Systems Science, and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190, China |
References:
[1] |
S. Chandrasekhar, The dynamics of stellar systems. I-VIII, Astrophys. J., 90 (1939), 1-154.
doi: 10.1086/144094. |
[2] |
A. Cheng, D. Coutand and S. Shkoller, On the motion of vortex sheets with surface tension in three-dimensional Euler equations with vorticity, Comm. Pure Appl. Math., 61 (2008), 1715-1752.
doi: 10.1002/cpa.20240. |
[3] |
R. Courant and K. O. Friedrichs, Supersonic Flow and Shock Waves, Springer-Verlag, New York, 1976. |
[4] |
D. Coutand, H. Lindblad and S. Shkoller, A priori estimates for the free-boundary 3D compressible Euler equations in physical vacuum, Comm. Math. Phys., 296 (2010), 559-587.
doi: 10.1007/s00220-010-1028-5. |
[5] |
D. Coutand and S. Shkoller, The interaction between quasilinear elastodynamics and the Navier-Stokes equations, Arch. Ration. Mech. Anal., 179 (2006), 303-352.
doi: 10.1007/s00205-005-0385-2. |
[6] |
D. Coutand and S. Shkoller, Well-posedness in smooth function spaces for moving-boundary 1-D compressible Euler equations in physical vacuum, Comm. Pure Appl. Math., 64 (2011), 328-366.
doi: 10.1002/cpa.20344. |
[7] |
D. Coutand and S. Shkoller, Well-posedness in smooth function spaces for the moving-boundary three-dimensional compressible Euler equations in physical vacuum, Arch. Rational Mech. Anal., 206 (2012), 515-616.
doi: 10.1007/s00205-012-0536-1. |
[8] |
J. P. Cox and R. T. Giuli, Principles of Stellar Structure, I, II, New York: Gordon and Breach, 1968. |
[9] |
J. Jang and N. Masmoudi, Well-posedness for compressible Euler equations with physical vacuum singularity, Comm. Pure Appl. Math., 62 (2009), 1327-1385.
doi: 10.1002/cpa.20285. |
[10] |
J. Jang and N. Masmoudi, Well-posedness of compressible Euler equations in a physical vacuum, Comm. Pure Appl. Math., 68 (2015), 61-111.
doi: 10.1002/cpa.21517. |
[11] |
H. O. Kreiss, Initial boundary value problems for hyperbolic systems, Comm. Pure Appl. Math., 23 (1970), 277-298.
doi: 10.1002/cpa.3160230304. |
[12] |
A. Kufner, Weighted Sobolev Spaces, A Wiley-Interscience Publication, John Wiley & Sons Inc., New York, 1985. |
[13] |
H. Lindblad, Well posedness for the motion of a compressible liquid with free surface boundary, Comm. Math. Phys., 260 (2005), 319-392.
doi: 10.1007/s00220-005-1406-6. |
[14] |
T. P. Liu, Compressible flow with damping and vacuum, Japan J. Indust. Appl. Math., 13 (1996), 25-32.
doi: 10.1007/BF03167296. |
[15] |
T. P. Liu and T. Yang, Compressible Euler equations with vacuum, J. Differential Equations, 140 (1997), 223-237.
doi: 10.1006/jdeq.1997.3281. |
[16] |
T. P. Liu and T. Yang, Compressible flow with vacuum and physical singularity, Methods Appl. Anal., 7 (2000), 495-509. |
[17] |
T. Luo, Z. Xin and H. Zeng, Well-posedness for the motion of physical vacuum of the three-dimensional compressible Euler equations with or without self-gravitation, Arch. Ration. Mech. Anal., 213 (2014), 763-831.
doi: 10.1007/s00205-014-0742-0. |
[18] |
T. Makino, On a local existence theorem for the evolution equation of gaseous stars, in Patterns and waves, vol. 18 of Stud. Math. Appl., North-Holland, Amsterdam, (1986), 459-479.
doi: 10.1016/S0168-2024(08)70142-5. |
[19] |
R. Temam, Navier-Stokes Equations, vol. 2 of Studies in Mathematics and its Applications, 3rd edition, North-Holland Publishing Co., Amsterdam, 1984. |
[20] |
Y. Trakhinin, Local existence for the free boundary problem for nonrelativistic and relativistic compressible Euler equations with a vacuum boundary condition, Comm. Pure Appl. Math., 62 (2009), 1551-1594.
doi: 10.1002/cpa.20282. |
[21] |
T. Yang, Singular behavior of vacuum states for compressible fluids, J. Comput. Appl. Math., 190 (2006), 211-231.
doi: 10.1016/j.cam.2005.01.043. |
show all references
References:
[1] |
S. Chandrasekhar, The dynamics of stellar systems. I-VIII, Astrophys. J., 90 (1939), 1-154.
doi: 10.1086/144094. |
[2] |
A. Cheng, D. Coutand and S. Shkoller, On the motion of vortex sheets with surface tension in three-dimensional Euler equations with vorticity, Comm. Pure Appl. Math., 61 (2008), 1715-1752.
doi: 10.1002/cpa.20240. |
[3] |
R. Courant and K. O. Friedrichs, Supersonic Flow and Shock Waves, Springer-Verlag, New York, 1976. |
[4] |
D. Coutand, H. Lindblad and S. Shkoller, A priori estimates for the free-boundary 3D compressible Euler equations in physical vacuum, Comm. Math. Phys., 296 (2010), 559-587.
doi: 10.1007/s00220-010-1028-5. |
[5] |
D. Coutand and S. Shkoller, The interaction between quasilinear elastodynamics and the Navier-Stokes equations, Arch. Ration. Mech. Anal., 179 (2006), 303-352.
doi: 10.1007/s00205-005-0385-2. |
[6] |
D. Coutand and S. Shkoller, Well-posedness in smooth function spaces for moving-boundary 1-D compressible Euler equations in physical vacuum, Comm. Pure Appl. Math., 64 (2011), 328-366.
doi: 10.1002/cpa.20344. |
[7] |
D. Coutand and S. Shkoller, Well-posedness in smooth function spaces for the moving-boundary three-dimensional compressible Euler equations in physical vacuum, Arch. Rational Mech. Anal., 206 (2012), 515-616.
doi: 10.1007/s00205-012-0536-1. |
[8] |
J. P. Cox and R. T. Giuli, Principles of Stellar Structure, I, II, New York: Gordon and Breach, 1968. |
[9] |
J. Jang and N. Masmoudi, Well-posedness for compressible Euler equations with physical vacuum singularity, Comm. Pure Appl. Math., 62 (2009), 1327-1385.
doi: 10.1002/cpa.20285. |
[10] |
J. Jang and N. Masmoudi, Well-posedness of compressible Euler equations in a physical vacuum, Comm. Pure Appl. Math., 68 (2015), 61-111.
doi: 10.1002/cpa.21517. |
[11] |
H. O. Kreiss, Initial boundary value problems for hyperbolic systems, Comm. Pure Appl. Math., 23 (1970), 277-298.
doi: 10.1002/cpa.3160230304. |
[12] |
A. Kufner, Weighted Sobolev Spaces, A Wiley-Interscience Publication, John Wiley & Sons Inc., New York, 1985. |
[13] |
H. Lindblad, Well posedness for the motion of a compressible liquid with free surface boundary, Comm. Math. Phys., 260 (2005), 319-392.
doi: 10.1007/s00220-005-1406-6. |
[14] |
T. P. Liu, Compressible flow with damping and vacuum, Japan J. Indust. Appl. Math., 13 (1996), 25-32.
doi: 10.1007/BF03167296. |
[15] |
T. P. Liu and T. Yang, Compressible Euler equations with vacuum, J. Differential Equations, 140 (1997), 223-237.
doi: 10.1006/jdeq.1997.3281. |
[16] |
T. P. Liu and T. Yang, Compressible flow with vacuum and physical singularity, Methods Appl. Anal., 7 (2000), 495-509. |
[17] |
T. Luo, Z. Xin and H. Zeng, Well-posedness for the motion of physical vacuum of the three-dimensional compressible Euler equations with or without self-gravitation, Arch. Ration. Mech. Anal., 213 (2014), 763-831.
doi: 10.1007/s00205-014-0742-0. |
[18] |
T. Makino, On a local existence theorem for the evolution equation of gaseous stars, in Patterns and waves, vol. 18 of Stud. Math. Appl., North-Holland, Amsterdam, (1986), 459-479.
doi: 10.1016/S0168-2024(08)70142-5. |
[19] |
R. Temam, Navier-Stokes Equations, vol. 2 of Studies in Mathematics and its Applications, 3rd edition, North-Holland Publishing Co., Amsterdam, 1984. |
[20] |
Y. Trakhinin, Local existence for the free boundary problem for nonrelativistic and relativistic compressible Euler equations with a vacuum boundary condition, Comm. Pure Appl. Math., 62 (2009), 1551-1594.
doi: 10.1002/cpa.20282. |
[21] |
T. Yang, Singular behavior of vacuum states for compressible fluids, J. Comput. Appl. Math., 190 (2006), 211-231.
doi: 10.1016/j.cam.2005.01.043. |
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