A shallow water modeling with the Coriolis effect coupled with the surface tension

Berjawi, Marwa; Elarwadi, Toufic; Israwi, Samer

doi:10.1007/s00605-022-01772-4

Cited by 2 publications

(4 citation statements)

References 33 publications

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“…To obtain an expression of (𝜕 𝑧 𝜑) | 𝑧=𝜀𝜁 , multiply (18) with 𝜇𝜀𝜁 𝑥 and do some calculations to get…”

Section: Zakharov Modelmentioning

confidence: 99%

“…Start with 𝐴 411 , one may proceed as in [18] and use the expression of  then use Kato-Ponce commutator estimate and hence the properties ( 35) and (37) to get…”

Section: Estimate Of ([λ 𝑠 𝐴[𝑈]]𝑈 𝑥 𝑆λ 𝑠 𝑈)mentioning

confidence: 99%

“…Use the estimates (35) and (36) and Moser inequality right after Kato-Ponce commutator estimate and then proceed as in [18] to get…”

Section: Estimate Of ([λ 𝑠 𝐴[𝑈]]𝑈 𝑥 𝑆λ 𝑠 𝑈)mentioning

confidence: 99%

“…It was rigorously justified that the solutions of the rotation Green-Naghdi system in the general initial data setting are well approximated in [17]. Lastly, a new idea was introduced in [18], where Coriolis effect and the surface tension were considered together to study the motion of water waves: a Green-Naghdi model of equations was formally derived and its well-posedness was studied, with flat bottom that is…”

Section: Introductionmentioning

confidence: 99%

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Well‐posedness of the Green–Naghdi model for an uneven bottom in presence of the Coriolis effect and surface tension

Berjawi,

El Arwadi,

Israwi

et al. 2024

Stud Appl Math

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The objective of this work is to derive and analyze a Green–Naghdi model with Coriolis effect and surface tension in nonflat bottom geometry. Gui et al. derive a Green–Naghdi‐type model in flat bottom geometry under the gravity and Coriolis effect. Chen et al. proved the existence and uniqueness of solution in Sobolev space under a condition depending on the initial velocity and the Coriolis effect. In this paper, we provide a rigorous derivation of Green–Naghdi model under the influence of the two mentioned effects, with nonflat bottom. After that, the existence and construction of solutions for the derived model will be proved under two alternative conditions: the first one is the same condition as in Chen et al. and Berjawi et al. and the second one concerns only the Coriolis coefficient that supposed to be only of order . This existence and uniqueness result ameliorate the result of Chen et al. and Berjawi et al. in the sense that no condition on the velocity is needed. We also prove the continuity of the associated flow map.

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“…To obtain an expression of (𝜕 𝑧 𝜑) | 𝑧=𝜀𝜁 , multiply (18) with 𝜇𝜀𝜁 𝑥 and do some calculations to get…”

Section: Zakharov Modelmentioning

confidence: 99%

“…Start with 𝐴 411 , one may proceed as in [18] and use the expression of  then use Kato-Ponce commutator estimate and hence the properties ( 35) and (37) to get…”

Section: Estimate Of ([λ 𝑠 𝐴[𝑈]]𝑈 𝑥 𝑆λ 𝑠 𝑈)mentioning

confidence: 99%

“…Use the estimates (35) and (36) and Moser inequality right after Kato-Ponce commutator estimate and then proceed as in [18] to get…”

Section: Estimate Of ([λ 𝑠 𝐴[𝑈]]𝑈 𝑥 𝑆λ 𝑠 𝑈)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Well‐posedness of the Green–Naghdi model for an uneven bottom in presence of the Coriolis effect and surface tension

Berjawi,

El Arwadi,

Israwi

et al. 2024

Stud Appl Math

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show abstract

Improved local existence result of the Green–Naghdi equations with the Coriolis effect

Khorbatly

2024

Nonlinear Analysis

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A shallow water modeling with the Coriolis effect coupled with the surface tension

Cited by 2 publications

References 33 publications

Well‐posedness of the Green–Naghdi model for an uneven bottom in presence of the Coriolis effect and surface tension

Well‐posedness of the Green–Naghdi model for an uneven bottom in presence of the Coriolis effect and surface tension

Improved local existence result of the Green–Naghdi equations with the Coriolis effect

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