Research output: Contribution to journal › Article › peer-review
On behaviour of free-surface profiles for bounded steady water waves. / Kozlov, V.; Kuznetsov, N.
In: Journal des Mathematiques Pures et Appliquees, Vol. 90, No. 1, 07.2008, p. 1-14.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - On behaviour of free-surface profiles for bounded steady water waves
AU - Kozlov, V.
AU - Kuznetsov, N.
N1 - Funding Information: V.K. was supported by the Swedish Research Council (VR). N.K. acknowledges the financial support from the Royal Swedish Academy of Sciences.
PY - 2008/7
Y1 - 2008/7
N2 - The paper deals with the classical non-linear problem of steady two-dimensional waves on water of finite depth. The problem is formulated so that it describes all waves without stagnation points on the free-surface profiles that are bounded themselves and have bounded slopes. By virtue of reducing the problem to an integro-differential equation the following three results are proved. First, there are no waves when the flow is critical. Second, there are no waves having profiles totally above the upper boundary of the uniform subcritical stream. Finally, only two types of the free-surface behaviour are possible at positive (or/and negative) infinity: the profile either oscillates infinitely many times around the upper boundary of the subcritical uniform stream or asymptotes the upper level of a uniform stream (subcritical or supercritical). The latter assertion is proved under additional assumption that the slope of the free surface is a uniformly continuous function.
AB - The paper deals with the classical non-linear problem of steady two-dimensional waves on water of finite depth. The problem is formulated so that it describes all waves without stagnation points on the free-surface profiles that are bounded themselves and have bounded slopes. By virtue of reducing the problem to an integro-differential equation the following three results are proved. First, there are no waves when the flow is critical. Second, there are no waves having profiles totally above the upper boundary of the uniform subcritical stream. Finally, only two types of the free-surface behaviour are possible at positive (or/and negative) infinity: the profile either oscillates infinitely many times around the upper boundary of the subcritical uniform stream or asymptotes the upper level of a uniform stream (subcritical or supercritical). The latter assertion is proved under additional assumption that the slope of the free surface is a uniformly continuous function.
KW - Finite depth
KW - Non-existence
KW - Steady water waves
KW - Subcritical flow
UR - http://www.scopus.com/inward/record.url?scp=50349092088&partnerID=8YFLogxK
U2 - 10.1016/j.matpur.2008.02.013
DO - 10.1016/j.matpur.2008.02.013
M3 - Article
AN - SCOPUS:50349092088
VL - 90
SP - 1
EP - 14
JO - Journal des Mathematiques Pures et Appliquees
JF - Journal des Mathematiques Pures et Appliquees
SN - 0021-7824
IS - 1
ER -
ID: 95240530