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Passive scalars, moving boundaries, and Newton's law of cooling
1. | Department of Mathematics, University of California, Riverside, Riverside, CA 92521 |
2. | Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, United States |
References:
[1] |
J. Beale, Large-time regularity of viscous surface waves,, Arch. Rational Mech. Anal., 84 (): 307.
doi: 10.1007/BF00250586. |
[2] |
J. Beale and T. Nishida, Large-time behavior of viscous surface waves, Recent topics in nonlinear PDE, II (Sendai, 1984), 1-14, North-Holland Math. Stud., 128, North-Holland, Amsterdam, 1985.
doi: 10.1016/S0304-0208(08)72355-7. |
[3] |
P. Constantin, A. Kiselev, L. Ryzhik and A. Zlatoš, Diffusion and mixing in fluid flow, Ann. of Math. (2), 168 (2008), 643-674.
doi: 10.4007/annals.2008.168.643. |
[4] |
A. Kiselev, R. Shterenberg and A. Zlatoš, Relaxation enhancement by time-periodic flows, Indiana Univ. Math. J., 57 (2008), 2137-2152.
doi: 10.1512/iumj.2008.57.3349. |
[5] |
Y. Guo and I. Tice, Almost exponential decay of periodic viscous surface waves without surface tension, Arch. Rational Mech. Anal., 207 (2013), 459-531.
doi: 10.1007/s00205-012-0570-z. |
[6] |
Y. Guo and I. Tice, Decay of viscous surface waves without surface tension in horizontally infinite domains, Anal. PDE, 6 (2013), 1429-1533.
doi: 10.2140/apde.2013.6.1429. |
[7] |
Y. Guo and I. Tice, Local well-posedness of the viscous surface wave problem without surface tension, Anal. PDE, 6 (2013), 287-369.
doi: 10.2140/apde.2013.6.287. |
[8] |
Y. Guo and Y. Wang, Decay of dissipative equations and negative Sobolev spaces, Comm. Partial Differential Equations, 37 (2012), 2165-2208.
doi: 10.1080/03605302.2012.696296. |
[9] |
Z. Lin, J.-L. Thiffeault and C. Doering, Optimal stirring strategies for passive scalar mixing, J. Fluid Mech., 675 (2011), 465-476.
doi: 10.1017/S0022112011000292. |
[10] |
A. Majda and P. Kramer, Simplified models for turbulent diffusion: Theory, numerical modelling, and physical phenomena, Phys. Rep., 314 (1999), 237-574.
doi: 10.1016/S0370-1573(98)00083-0. |
[11] |
T. Nishida, Y. Teramoto and H. Yoshihara, Global in time behavior of viscous surface waves: Horizontally periodic motion, J. Math. Kyoto Univ., 44 (2004), 271-323. |
[12] |
J. Slattery, Advanced Transport Phenomena, Cambridge University Press, Cambridge, 1999. |
[13] |
W. Strauss, Partial Differential Equations. An Introduction, John Wiley and Sons, Inc., New York, 1992. |
[14] |
J.-L. Thiffeault, Using multiscale norms to quantify mixing and transport, Nonlinearity, 25 (2012), R1-R44.
doi: 10.1088/0951-7715/25/2/R1. |
[15] |
Z. Warhaft, Passive scalars in turbulent flows, Annu. Rev. Fluid Mech., 32 (2000), 203-240.
doi: 10.1146/annurev.fluid.32.1.203. |
[16] |
A. Zlatoš, Diffusion in fluid flow: Dissipation enhancement by flows in 2D, Comm. Partial Differential Equations, 35 (2010), 496-534.
doi: 10.1080/03605300903362546. |
show all references
References:
[1] |
J. Beale, Large-time regularity of viscous surface waves,, Arch. Rational Mech. Anal., 84 (): 307.
doi: 10.1007/BF00250586. |
[2] |
J. Beale and T. Nishida, Large-time behavior of viscous surface waves, Recent topics in nonlinear PDE, II (Sendai, 1984), 1-14, North-Holland Math. Stud., 128, North-Holland, Amsterdam, 1985.
doi: 10.1016/S0304-0208(08)72355-7. |
[3] |
P. Constantin, A. Kiselev, L. Ryzhik and A. Zlatoš, Diffusion and mixing in fluid flow, Ann. of Math. (2), 168 (2008), 643-674.
doi: 10.4007/annals.2008.168.643. |
[4] |
A. Kiselev, R. Shterenberg and A. Zlatoš, Relaxation enhancement by time-periodic flows, Indiana Univ. Math. J., 57 (2008), 2137-2152.
doi: 10.1512/iumj.2008.57.3349. |
[5] |
Y. Guo and I. Tice, Almost exponential decay of periodic viscous surface waves without surface tension, Arch. Rational Mech. Anal., 207 (2013), 459-531.
doi: 10.1007/s00205-012-0570-z. |
[6] |
Y. Guo and I. Tice, Decay of viscous surface waves without surface tension in horizontally infinite domains, Anal. PDE, 6 (2013), 1429-1533.
doi: 10.2140/apde.2013.6.1429. |
[7] |
Y. Guo and I. Tice, Local well-posedness of the viscous surface wave problem without surface tension, Anal. PDE, 6 (2013), 287-369.
doi: 10.2140/apde.2013.6.287. |
[8] |
Y. Guo and Y. Wang, Decay of dissipative equations and negative Sobolev spaces, Comm. Partial Differential Equations, 37 (2012), 2165-2208.
doi: 10.1080/03605302.2012.696296. |
[9] |
Z. Lin, J.-L. Thiffeault and C. Doering, Optimal stirring strategies for passive scalar mixing, J. Fluid Mech., 675 (2011), 465-476.
doi: 10.1017/S0022112011000292. |
[10] |
A. Majda and P. Kramer, Simplified models for turbulent diffusion: Theory, numerical modelling, and physical phenomena, Phys. Rep., 314 (1999), 237-574.
doi: 10.1016/S0370-1573(98)00083-0. |
[11] |
T. Nishida, Y. Teramoto and H. Yoshihara, Global in time behavior of viscous surface waves: Horizontally periodic motion, J. Math. Kyoto Univ., 44 (2004), 271-323. |
[12] |
J. Slattery, Advanced Transport Phenomena, Cambridge University Press, Cambridge, 1999. |
[13] |
W. Strauss, Partial Differential Equations. An Introduction, John Wiley and Sons, Inc., New York, 1992. |
[14] |
J.-L. Thiffeault, Using multiscale norms to quantify mixing and transport, Nonlinearity, 25 (2012), R1-R44.
doi: 10.1088/0951-7715/25/2/R1. |
[15] |
Z. Warhaft, Passive scalars in turbulent flows, Annu. Rev. Fluid Mech., 32 (2000), 203-240.
doi: 10.1146/annurev.fluid.32.1.203. |
[16] |
A. Zlatoš, Diffusion in fluid flow: Dissipation enhancement by flows in 2D, Comm. Partial Differential Equations, 35 (2010), 496-534.
doi: 10.1080/03605300903362546. |
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