On the Symmetry and Recovery of Steady Continuously Stratified Periodic Water Waves

Xu, Fei; Zhang, Yong; Li, Fengquan

doi:10.1007/s00021-021-00614-x

Cited by 3 publications

(2 citation statements)

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“…Remark 3.5. : In particular, if choosing σ = 0 in this case, the symmetry result is consistent with the recent work [6].…”

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confidence: 91%

“…By introducing hodograph transformation, the result was further improved in [5] for any arbitrary vorticity functions. Following the breakthrough work in [5], the symmetry properties of periodic water waves have been extended to more general rotational flows, such as flows are stratified [3,6], or with negative surface tension [19] and flows are near equatorial region [20,29], or with arbitrarily many crests and troughs [28]. Besides, the moving plane method was also applied to investigate the symmetry properties of gravity solitary waves in [22,23].…”

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confidence: 99%

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The symmetry for two class of steady stratified periodic water waves

Li¹,

Fei²,

Zhang³

2022

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In this paper, we mainly consider two class of travelling stratified periodic water waves, one with negative (or without) surface tension and the other with constant Bernoulli's function and stagnation points. We first establish the symmetry result for stratified water waves with negative (or without) surface tension, but without stagnation by using the modified maximum principle. Furthermore, the symmetry property of stratified water waves with constant Bernoulli's function and stagnation points is also obtained provided the monotonic property is known.

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“…Remark 3.5. : In particular, if choosing σ = 0 in this case, the symmetry result is consistent with the recent work [6].…”

Section: ) Follows Fromsupporting

confidence: 91%