Well-posedness for a two-dimensional dispersive model arising from capillary-gravity flows

Riaño, Oscar

doi:10.1016/j.jde.2021.01.021

Cited by 8 publications

(2 citation statements)

References 41 publications

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“…Brooke Benjamin 1967;Ono 1975) and Burgers-Hilbert equation (cf. Biello and Hunter 2010) (see also Riaño 2021). It is also similar to the equation derived in Durán (2020).…”

Section: Derivationsupporting

confidence: 74%

On the Motion of Gravity–Capillary Waves with Odd Viscosity

Granero-Belinchón

Ortega

2022

J Nonlinear Sci

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We develop three asymptotic models of surface waves in a non-Newtonian fluid with odd viscosity. This viscosity is also known as Hall viscosity and appears in a number of applications such as quantum Hall fluids or chiral active fluids. Besides the odd viscosity effects, these models capture both gravity and capillary forces up to quadratic interactions and take the form of nonlinear and nonlocal wave equations. Two of these models describe bidirectional waves, while the third PDE studies the case of unidirectional propagation. We also prove the well-posedness of these asymptotic models in spaces of analytic functions and in Sobolev spaces. Finally, we present a number of numerical simulations for the unidirectional model.

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“…Brooke Benjamin 1967;Ono 1975) and Burgers-Hilbert equation (cf. Biello and Hunter 2010) (see also Riaño 2021). It is also similar to the equation derived in Durán (2020).…”

Section: Derivationsupporting

confidence: 74%

On the Motion of Gravity–Capillary Waves with Odd Viscosity

Granero-Belinchón

Ortega

2022

J Nonlinear Sci

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“…The inequality (2.8) was established in [7, lemma 3.1]. We refer to [40] for a proof of (2.9). We also require the following fractional commutator estimate for the Hilbert transform.…”

Section: Leibniz Rule and Commutator Estimatesmentioning

confidence: 93%

On persistence properties in weighted spaces for solutions of the fractional Korteweg–de Vries equation

Riaño

2021

Nonlinearity

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Persistence problems in weighted spaces have been studied for different dispersive models involving non-local operators. Generally, these models do not propagate polynomial weights of arbitrary magnitude, and the maximum decay rate is associated with the dispersive part of the equation. Altogether, this analysis is complemented by unique continuation principles that determine optimal spatial decay. This work is intended to establish the above questions for a weakly dispersive perturbation of the inviscid Burgers equation. More precisely, we consider the fractional Korteweg–de Vries equation, which comprises the Burgers–Hilbert equation and dispersive effects weaker than those of the Benjamin–Ono equation.

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On well-posed isoperimetric-type constrained variational control problems

Treanţă

2021

Journal of Differential Equations

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Well-posedness for a two-dimensional dispersive model arising from capillary-gravity flows

Cited by 8 publications

References 41 publications

On the Motion of Gravity–Capillary Waves with Odd Viscosity

On the Motion of Gravity–Capillary Waves with Odd Viscosity

On persistence properties in weighted spaces for solutions of the fractional Korteweg–de Vries equation

On well-posed isoperimetric-type constrained variational control problems

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