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Volumn 148, Issue 12, 2020, Pages 5181-5191

Well-posedness of water wave model with viscous effects

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EID: 85084534853     PISSN: 00029939     EISSN: 10886826     Source Type: Journal    
DOI: 10.1090/proc/15219     Document Type: Article
Times cited : (13)

References (37)
  • 1
    • 77956246729 scopus 로고    scopus 로고
    • Dynamics of three-dimensional gravity-capillary solitary waves in deep water
    • MR2678044
    • Benjamin Akers and Paul A. Milewski, Dynamics of three-dimensional gravity-capillary solitary waves in deep water, SIAM J. Appl. Math. 70 (2010), no. 7, 2390–2408, DOI 10.1137/090758386. MR2678044
    • (2010) SIAM J. Appl. Math , vol.70 , Issue.7 , pp. 2390-2408
    • Akers, Benjamin1    Milewski, Paul A.2
  • 2
    • 77956241032 scopus 로고    scopus 로고
    • Traveling waves in deep water with gravity and surface tension
    • MR2678043
    • Benjamin Akers and David P. Nicholls, Traveling waves in deep water with gravity and surface tension, SIAM J. Appl. Math. 70 (2010), no. 7, 2373–2389, DOI 10.1137/090771351. MR2678043
    • (2010) SIAM J. Appl. Math , vol.70 , Issue.7 , pp. 2373-2389
    • Akers, Benjamin1    Nicholls, David P.2
  • 3
    • 84861694721 scopus 로고    scopus 로고
    • Well-posedness of a model for water waves with viscosity
    • MR2899939
    • David M. Ambrose, Jerry L. Bona, and David P. Nicholls, Well-posedness of a model for water waves with viscosity, Discrete Contin. Dyn. Syst. Ser. B 17 (2012), no. 4, 1113–1137, DOI 10.3934/dcdsb.2012.17.1113. MR2899939
    • (2012) Discrete Contin. Dyn. Syst. Ser. B , vol.17 , Issue.4 , pp. 1113-1137
    • Ambrose, David M.1    Bona, Jerry L.2    Nicholls, David P.3
  • 4
    • 34447634692 scopus 로고
    • Lois de l’extinction de la houle en haute mer
    • J. Boussinesq, Lois de l’extinction de la houle en haute mer, C. R. Acad. Sci. Paris 121 (1895), no. 2, 15–20.
    • (1895) C. R. Acad. Sci. Paris , vol.121 , Issue.2 , pp. 15-20
    • Boussinesq, J.1
  • 5
    • 84942354084 scopus 로고    scopus 로고
    • Well-posedness of the Muskat problem with H2 initial data
    • MR3415681
    • C. H. Arthur Cheng, Rafael Granero-Belinchón, and Steve Shkoller, Well-posedness of the Muskat problem with H2 initial data, Adv. Math. 286 (2016), 32–104, DOI 10.1016/j.aim.2015.08.026. MR3415681
    • (2016) Adv. Math , vol.286 , pp. 32-104
    • Arthur Cheng, C. H.1    Granero-Belinchón, Rafael2    Shkoller, Steve3
  • 7
    • 0002686768 scopus 로고
    • Numerical simulation of gravity waves
    • MR1239970
    • W. Craig and C. Sulem, Numerical simulation of gravity waves, J. Comput. Phys. 108 (1993), no. 1, 73–83, DOI 10.1006/jcph.1993.1164. MR1239970
    • (1993) J. Comput. Phys , vol.108 , Issue.1 , pp. 73-83
    • Craig, W.1    Sulem, C.2
  • 8
    • 77950654121 scopus 로고    scopus 로고
    • On the decay properties of solutions to a class of Schrödinger equations
    • MR2383514
    • L. Dawson, H. McGahagan, and G. Ponce, On the decay properties of solutions to a class of Schrödinger equations, Proc. Amer. Math. Soc. 136 (2008), no. 6, 2081–2090, DOI 10.1090/S0002-9939-08-09355-6. MR2383514
    • (2008) Proc. Amer. Math. Soc , vol.136 , Issue.6 , pp. 2081-2090
    • Dawson, L.1    McGahagan, H.2    Ponce, G.3
  • 9
    • 38849134959 scopus 로고    scopus 로고
    • Theory of weakly damped free-surface flows: a new formulation based on potential flow solutions
    • Frederic Dias, Alexander I. Dyachenko, and Vladimir E. Zakharov, Theory of weakly damped free-surface flows: a new formulation based on potential flow solutions, Phys. Lett. A 372 (2008), no. 8, 1297–1302.
    • (2008) Phys. Lett. A , vol.372 , Issue.8 , pp. 1297-1302
    • Dias, Frederic1    Dyachenko, Alexander I.2    Zakharov, Vladimir E.3
  • 10
    • 62649165873 scopus 로고    scopus 로고
    • Visco-potential free-surface flows and long wave modelling
    • MR2513897
    • Denys Dutykh, Visco-potential free-surface flows and long wave modelling, Eur. J. Mech. B Fluids 28 (2009), no. 3, 430–443, DOI 10.1016/j.euromechflu.2008.11.003. MR2513897
    • (2009) Eur. J. Mech. B Fluids , vol.28 , Issue.3 , pp. 430-443
    • Dutykh, Denys1
  • 11
    • 35548942232 scopus 로고    scopus 로고
    • Dissipative Boussinesq equations
    • Denys Dutykh and Frédéric Dias, Dissipative Boussinesq equations, C. R. Mecanique 335 (2007), no. 9–10, 559–583.
    • (2007) C. R. Mecanique , vol.335 , Issue.9–10 , pp. 559-583
    • Dutykh, Denys1    Dias, Frédéric2
  • 12
    • 34447630128 scopus 로고    scopus 로고
    • Viscous potential free-surface flows in a fluid layer of finite depth (English, with English and French summaries)
    • MR2343563
    • Denys Dutykh and Frédéric Dias, Viscous potential free-surface flows in a fluid layer of finite depth (English, with English and French summaries), C. R. Math. Acad. Sci. Paris 345 (2007), no. 2, 113–118, DOI 10.1016/j.crma.2007.06.007. MR2343563
    • (2007) C. R. Math. Acad. Sci. Paris , vol.345 , Issue.2 , pp. 113-118
    • Dutykh, Denys1    Dias, Frédéric2
  • 13
    • 84899042580 scopus 로고    scopus 로고
    • Derivation of dissipative Boussinesq equations using the Dirichlet-to-Neumann operator approach
    • MR3501289
    • Denys Dutykh and Olivier Goubet, Derivation of dissipative Boussinesq equations using the Dirichlet-to-Neumann operator approach, Math. Comput. Simulation 127 (2016), 80–93, DOI 10.1016/j.matcom.2013.12.008. MR3501289
    • (2016) Math. Comput. Simulation , vol.127 , pp. 80-93
    • Dutykh, Denys1    Goubet, Olivier2
  • 14
    • 84899754405 scopus 로고    scopus 로고
    • The Kato-Ponce inequality
    • MR3200091
    • Loukas Grafakos and Seungly Oh, The Kato-Ponce inequality, Comm. Partial Differential Equations 39 (2014), no. 6, 1128–1157, DOI 10.1080/03605302.2013.822885. MR3200091
    • (2014) Comm. Partial Differential Equations , vol.39 , Issue.6 , pp. 1128-1157
    • Grafakos, Loukas1    Oh, Seungly2
  • 16
    • 85063264613 scopus 로고    scopus 로고
    • Asymptotic models for free boundary flow in porous media
    • MR3928312
    • Rafael Granero-Belinchón and Stefano Scrobogna, Asymptotic models for free boundary flow in porous media, Phys. D 392 (2019), 1–16, DOI 10.1016/j.physd.2019.02.013. MR3928312
    • (2019) Phys. D , vol.392 , pp. 1-16
    • Granero-Belinchón, Rafael1    Scrobogna, Stefano2
  • 17
    • 85076878639 scopus 로고    scopus 로고
    • Models for damped water waves
    • MR4041720
    • Rafael Granero-Belinchón and Stefano Scrobogna, Models for damped water waves, SIAM J. Appl. Math. 79 (2019), no. 6, 2530–2550, DOI 10.1137/19M1262899. MR4041720
    • (2019) SIAM J. Appl. Math , vol.79 , Issue.6 , pp. 2530-2550
    • Granero-Belinchón, Rafael1    Scrobogna, Stefano2
  • 19
    • 85016981628 scopus 로고    scopus 로고
    • A model for Rayleigh-Taylor mixing and interface turnover
    • MR3612171
    • Rafael Granero-Belinchón and Steve Shkoller, A model for Rayleigh-Taylor mixing and interface turnover, Multiscale Model. Simul. 15 (2017), no. 1, 274–308, DOI 10.1137/16M1083463. MR3612171
    • (2017) Multiscale Model. Simul , vol.15 , Issue.1 , pp. 274-308
    • Granero-Belinchón, Rafael1    Shkoller, Steve2
  • 20
    • 0030403292 scopus 로고    scopus 로고
    • Moderate and steep Faraday waves: instabilities, modulation and temporal asymmetries
    • Lei Jiang, Chao-Lung Ting, Marc Perlin, and William W. Schultz, Moderate and steep Faraday waves: instabilities, modulation and temporal asymmetries, J. Fluid Mech. 329 (1996), 275–307.
    • (1996) J. Fluid Mech , vol.329 , pp. 275-307
    • Jiang, Lei1    Ting, Chao-Lung2    Perlin, Marc3    Schultz, William W.4
  • 21
    • 2442660045 scopus 로고    scopus 로고
    • The dissipation approximation and viscous potential flow
    • MR2259003
    • D. D. Joseph and J. Wang, The dissipation approximation and viscous potential flow, J. Fluid Mech. 505 (2004), 365–377, DOI 10.1017/S0022112004008602. MR2259003
    • (2004) J. Fluid Mech , vol.505 , pp. 365-377
    • Joseph, D. D.1    Wang, J.2
  • 22
    • 77951104207 scopus 로고    scopus 로고
    • Numerical simulation of a weakly nonlinear model for water waves with viscosity
    • MR2578037
    • Maria Kakleas and David P. Nicholls, Numerical simulation of a weakly nonlinear model for water waves with viscosity, J. Sci. Comput. 42 (2010), no. 2, 274–290, DOI 10.1007/s10915-009-9324-y. MR2578037
    • (2010) J. Sci. Comput , vol.42 , Issue.2 , pp. 274-290
    • Kakleas, Maria1    Nicholls, David P.2
  • 23
    • 84990617895 scopus 로고
    • Commutator estimates and the Euler and Navier-Stokes equations
    • MR951744
    • Tosio Kato and Gustavo Ponce, Commutator estimates and the Euler and Navier-Stokes equations, Comm. Pure Appl. Math. 41 (1988), no. 7, 891–907, DOI 10.1002/cpa.3160410704. MR951744
    • (1988) Comm. Pure Appl. Math , vol.41 , Issue.7 , pp. 891-907
    • Kato, Tosio1    Ponce, Gustavo2
  • 24
    • 84990553608 scopus 로고
    • Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle
    • MR1211741
    • Carlos E. Kenig, Gustavo Ponce, and Luis Vega, Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle, Comm. Pure Appl. Math. 46 (1993), no. 4, 527–620, DOI 10.1002/cpa.3160460405. MR1211741
    • (1993) Comm. Pure Appl. Math , vol.46 , Issue.4 , pp. 527-620
    • Kenig, Carlos E.1    Ponce, Gustavo2    Vega, Luis3
  • 25
    • 0000691222 scopus 로고    scopus 로고
    • Nonlinear evolution of water surface waves: the frequency down-shift phenomenon, Mathematical problems in the theory of water waves (Luminy, 1995)
    • Amer. Math. Soc., Providence, RI, MR1410506
    • C. Skandrani, C. Kharif, and J. Poitevin, Nonlinear evolution of water surface waves: the frequency down-shift phenomenon, Mathematical problems in the theory of water waves (Luminy, 1995), Contemp. Math., vol. 200, Amer. Math. Soc., Providence, RI, 1996, pp. 157–171, DOI 10.1090/conm/200/02514. MR1410506
    • (1996) Contemp. Math , vol.200 , pp. 157-171
    • Skandrani, C.1    Kharif, C.2    Poitevin, J.3
  • 26
    • 0004168443 scopus 로고
    • 6th ed., with a foreword by R. A. Caflisch [Russel E. Caflisch], Cambridge Mathematical Library, Cambridge University Press, Cambridge, MR1317348
    • Horace Lamb, Hydrodynamics, 6th ed., with a foreword by R. A. Caflisch [Russel E. Caflisch], Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1993. MR1317348
    • (1993) Hydrodynamics
    • Lamb, Horace1
  • 27
    • 0026796993 scopus 로고
    • Theory of weakly damped Stokes waves: a new formulation and its physical interpretation
    • MR1150193
    • Michael S. Longuet-Higgins, Theory of weakly damped Stokes waves: a new formulation and its physical interpretation, J. Fluid Mech. 235 (1992), 319–324, DOI 10.1017/S0022112092001125. MR1150193
    • (1992) J. Fluid Mech , vol.235 , pp. 319-324
    • Longuet-Higgins, Michael S.1
  • 28
    • 0038123824 scopus 로고
    • Nonlinear evolutions of surface gravity waves on fluid of finite depth
    • Y Matsuno Nonlinear evolutions of surface gravity waves on fluid of finite depth. Physical review letters, 69(4):609, 1992.
    • (1992) Physical review letters , vol.69 , Issue.4 , pp. 609
    • Matsuno, Y1
  • 29
    • 0027396327 scopus 로고
    • Nonlinear evolution of surface gravity waves over an uneven bottom
    • MR1214472
    • Y. Matsuno, Nonlinear evolution of surface gravity waves over an uneven bottom, J. Fluid Mech. 249 (1993), 121–133, DOI 10.1017/S0022112093001107. MR1214472
    • (1993) J. Fluid Mech , vol.249 , pp. 121-133
    • Matsuno, Y.1
  • 30
    • 0344639081 scopus 로고
    • Two-dimensional evolution of surface gravity waves on a fluid of arbitrary depth
    • Yoshimasa Matsuno, Two-dimensional evolution of surface gravity waves on a fluid of arbitrary depth, Physical Review E, 47(6):4593, 1993.
    • (1993) Physical Review E , vol.47 , Issue.6 , pp. 4593
    • Matsuno, Yoshimasa1
  • 31
    • 85048976819 scopus 로고    scopus 로고
    • Well-posedness and analyticity of solutions to a water wave problem with viscosity
    • MR3848244
    • Marième Ngom and David P. Nicholls, Well-posedness and analyticity of solutions to a water wave problem with viscosity, J. Differential Equations 265 (2018), no. 10, 5031–5065, DOI 10.1016/j.jde.2018.06.030. MR3848244
    • (2018) J. Differential Equations , vol.265 , Issue.10 , pp. 5031-5065
    • Ngom, Marième1    Nicholls, David P.2
  • 32
    • 0026219343 scopus 로고
    • Numerical simulations of the quasi-stationary stage of ripple excitation by steep gravity–capillary waves
    • K. D. Ruvinsky, F. I. Feldstein, and G. I. Freidman, Numerical simulations of the quasi-stationary stage of ripple excitation by steep gravity–capillary waves, J. Fluid Mech. 230 (1991), 339–353.
    • (1991) J. Fluid Mech , vol.230 , pp. 339-353
    • Ruvinsky, K. D.1    Feldstein, F. I.2    Freidman, G. I.3
  • 33
    • 84971864398 scopus 로고
    • Improvement of the first Stokes method for the investigation of finite-amplitude potential gravity-capillary waves
    • Tbilisi: Theses of Reports
    • K. D. Ruvinsky and G. I. Freidman, Improvement of the first Stokes method for the investigation of finite-amplitude potential gravity-capillary waves, IX All-Union Symp. on Diffraction and Propagation Waves, Tbilisi: Theses of Reports, volume 2, 1985, pp. 22–25.
    • (1985) IX All-Union Symp. on Diffraction and Propagation Waves , vol.2 , pp. 22-25
    • Ruvinsky, K. D.1    Freidman, G. I.2
  • 34
    • 84932645974 scopus 로고
    • The fine structure of strong gravity-capillary waves
    • AV Gaponov-Grekhov and MI Rabinovich, eds. Moscow: Nauka, pages
    • K. D. Ruvinsky and G. I. Freidman. The fine structure of strong gravity-capillary waves, Nonlinear waves: Structures and Bifurcations, AV Gaponov-Grekhov and MI Rabinovich, eds. Moscow: Nauka, pages 304–326, 1987.
    • (1987) Nonlinear waves: Structures and Bifurcations , pp. 304-326
    • Ruvinsky, K. D.1    Freidman, G. I.2
  • 35
    • 0040267906 scopus 로고
    • of Cambridge Library Collection Mathematics, Cambridge University Press
    • George Gabriel Stokes, On the Theory of Oscillatory Waves, volume 1 of Cambridge Library Collection - Mathematics, Cambridge University Press, 1847.
    • (1847) On the Theory of Oscillatory Waves , vol.1
    • Stokes, George Gabriel1
  • 36
    • 33244464033 scopus 로고    scopus 로고
    • Purely irrotational theories of the effect of the viscosity on the decay of free gravity waves
    • MR2266175
    • J. Wang and D. D. Joseph, Purely irrotational theories of the effect of the viscosity on the decay of free gravity waves, J. Fluid Mech. 559 (2006), 461–472, DOI 10.1017/S0022112006000401. MR2266175
    • (2006) J. Fluid Mech , vol.559 , pp. 461-472
    • Wang, J.1    Joseph, D. D.2
  • 37
    • 33744917573 scopus 로고    scopus 로고
    • A note on stabilizing the Benjamin-Feir instability
    • MR2263443
    • Guangyu Wu, Yuming Liu, and Dick K. P. Yue, A note on stabilizing the Benjamin-Feir instability, J. Fluid Mech. 556 (2006), 45–54, DOI 10.1017/S0022112005008293. MR2263443
    • (2006) J. Fluid Mech , vol.556 , pp. 45-54
    • Wu, Guangyu1    Liu, Yuming2    Yue, Dick K. P.3


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