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A note on uniqueness and compact support of solutions in a recent model for tsunami background flows
1.  Nordbergstrasse 15, UZA 2, 2A 287, 1090 Wien, Austria 
References:
[1] 
G. K. Batchelor, "An Introduction to Fluid Dynamics," Cambridge University Press, 1967. 
[2] 
E. Bryant, "Tsunami: The Underrated Hazard," Springer Praxis Books, Springer Berlin Heidelberg, 2008. 
[3] 
A. Constantin, The trajectories of particles in Stokes waves, Invent. Math., 166 (2006), 523535. 
[4] 
A. Constantin, On the propagation of tsunami waves, with emphasis on the tsunami of 2004, Discrete Contin. Dyn. Syst. Ser. B, 12 (2009), 525537. 
[5] 
A. Constantin, On the relevance of soliton theory to tsunami modelling, Wave Motion, 46 (2009), 420426. 
[6] 
A. Constantin, A dynamical systems approach towards isolated vorticity regions for tsunami background states, Arch. Ration. Mech. Anal., 200 (2011), 239253. 
[7] 
A. Constantin and J. Escher, Analyticity of periodic traveling free surface water waves with vorticity, Ann. of Math., 172 (2010), PAGES. 
[8] 
A. Constantin and D. Henry, Solitons and tsunamis, Z. Naturforsch., 64a (2009), 6568. 
[9] 
A. Constantin and R. S. Johnson, Modelling tsunamis, J. Phys. A, 39 (2006), L215L217. 
[10] 
A. Constantin and R. Johnson, Propagation of very long water waves, with vorticity, over variable depth, with applications to tsunamis, Fluid Dynamics Research, 40 (2008), 175211. 
[11] 
A. Constantin and R. S. Johnson, On the nondimensionalisation, scaling and resulting interpretation of the classical governing equations for water waves, J. Nonl. Math. Phys., 15 (2008), 5873. 
[12] 
A. Constantin and W. Strauss, Exact steady periodic water waves with vorticity, Comm. Pure Appl. Math., 57 (2004), 481527. 
[13] 
W. A. Coppel, "Stability and Asymptotic Behavior of Differential Equations," D. C. Heath and Co., Boston, Massachussetts, 1965. 
[14] 
W. Craig, Surface water waves and tsunamis, J. Dynam. Differential Equations, 18 (2006), 525549. 
[15] 
A. Geyer, On some background flows for tsunami waves, J. Math. Fluid Mech.. doi: DOI 10.1007/s0002101100550. 
[16] 
J. Hale, "Ordinary Differential Equations," Wiley, New York, 1969. 
[17] 
J. L. Hammack, A note on tsunamis: their generation and propagation in an ocean of uniform depth, J. Fluid Mech., 60 (1973), 769799. 
[18] 
R. S. Johnson, "A Modern Introduction to the Mathematical Theory of Water Waves," Cambridge University Press, Cambridge, 1997. 
[19] 
M. Lakshmanan, Integrable nonlinear wave equations and possible connections to tsunami dynamics, in "Tsunami and Nonlinear Waves" (A. Kundu ed.), Springer, Berlin (2007), 3149. 
[20] 
O. Mustafa, On the uniqueness of flow in a recent tsunami model, Applicable Analysis, 2011 doi: doi: 10.1080/00036811.2011.569499. 
[21] 
H. Segur, Waves in shallow water with emphasis on the tsunami of 2004, in "Tsunami and Nonlinear Waves" (A. Kundu ed.), Springer, Berlin (2007), 329. 
[22] 
R. Stuhlmeier, KdV theory and the Chilean tsunami of 1960, Discrete Contin. Dyn. Syst. Ser. B, 12 (2009), 623632. 
show all references
References:
[1] 
G. K. Batchelor, "An Introduction to Fluid Dynamics," Cambridge University Press, 1967. 
[2] 
E. Bryant, "Tsunami: The Underrated Hazard," Springer Praxis Books, Springer Berlin Heidelberg, 2008. 
[3] 
A. Constantin, The trajectories of particles in Stokes waves, Invent. Math., 166 (2006), 523535. 
[4] 
A. Constantin, On the propagation of tsunami waves, with emphasis on the tsunami of 2004, Discrete Contin. Dyn. Syst. Ser. B, 12 (2009), 525537. 
[5] 
A. Constantin, On the relevance of soliton theory to tsunami modelling, Wave Motion, 46 (2009), 420426. 
[6] 
A. Constantin, A dynamical systems approach towards isolated vorticity regions for tsunami background states, Arch. Ration. Mech. Anal., 200 (2011), 239253. 
[7] 
A. Constantin and J. Escher, Analyticity of periodic traveling free surface water waves with vorticity, Ann. of Math., 172 (2010), PAGES. 
[8] 
A. Constantin and D. Henry, Solitons and tsunamis, Z. Naturforsch., 64a (2009), 6568. 
[9] 
A. Constantin and R. S. Johnson, Modelling tsunamis, J. Phys. A, 39 (2006), L215L217. 
[10] 
A. Constantin and R. Johnson, Propagation of very long water waves, with vorticity, over variable depth, with applications to tsunamis, Fluid Dynamics Research, 40 (2008), 175211. 
[11] 
A. Constantin and R. S. Johnson, On the nondimensionalisation, scaling and resulting interpretation of the classical governing equations for water waves, J. Nonl. Math. Phys., 15 (2008), 5873. 
[12] 
A. Constantin and W. Strauss, Exact steady periodic water waves with vorticity, Comm. Pure Appl. Math., 57 (2004), 481527. 
[13] 
W. A. Coppel, "Stability and Asymptotic Behavior of Differential Equations," D. C. Heath and Co., Boston, Massachussetts, 1965. 
[14] 
W. Craig, Surface water waves and tsunamis, J. Dynam. Differential Equations, 18 (2006), 525549. 
[15] 
A. Geyer, On some background flows for tsunami waves, J. Math. Fluid Mech.. doi: DOI 10.1007/s0002101100550. 
[16] 
J. Hale, "Ordinary Differential Equations," Wiley, New York, 1969. 
[17] 
J. L. Hammack, A note on tsunamis: their generation and propagation in an ocean of uniform depth, J. Fluid Mech., 60 (1973), 769799. 
[18] 
R. S. Johnson, "A Modern Introduction to the Mathematical Theory of Water Waves," Cambridge University Press, Cambridge, 1997. 
[19] 
M. Lakshmanan, Integrable nonlinear wave equations and possible connections to tsunami dynamics, in "Tsunami and Nonlinear Waves" (A. Kundu ed.), Springer, Berlin (2007), 3149. 
[20] 
O. Mustafa, On the uniqueness of flow in a recent tsunami model, Applicable Analysis, 2011 doi: doi: 10.1080/00036811.2011.569499. 
[21] 
H. Segur, Waves in shallow water with emphasis on the tsunami of 2004, in "Tsunami and Nonlinear Waves" (A. Kundu ed.), Springer, Berlin (2007), 329. 
[22] 
R. Stuhlmeier, KdV theory and the Chilean tsunami of 1960, Discrete Contin. Dyn. Syst. Ser. B, 12 (2009), 623632. 
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