On a linearized system arising in the study of viscous surface flow down an inclined plane

Teramoto, Yoshikuni; Tomoeda, Kyoko

doi:10.1007/s11565-013-0198-4

Cited by 1 publication

(2 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Suppose that (v, q, ζ) solve (3.1), where Φ, A, J, etc are determined by η as in (1. 19) and (1.21). Then…”

Section: Evolution Of the Energy And Dissipationmentioning

confidence: 96%

“…Padula [12,13] studied the 3D problem with fixed positive surface tension and developed sufficient conditions for low-regularity asymptotic stability under the a priori assumption of the existence of global smooth solutions. Teramoto-Tomoeda [19] studied the linearized 2D problem with fixed positive surface tension and proved that the linearized problem generates an analytic semigroup, but they did not discuss the nonlinear theory. Nishida-Teramoto-Yoshihara [11] developed the Hopf bifurcation analysis for the 2D problem with fixed surface tension under some assumptions on the spectrum of the linearized operator in order to construct time periodic solutions.…”

Section: Eulerian Perturbationmentioning

confidence: 99%

See 1 more Smart Citation

Asymptotic stability of shear-flow solutions to incompressible viscous free boundary problems with and without surface tension

Tice

2018

Z. Angew. Math. Phys.

View full text Add to dashboard Cite

This paper concerns the dynamics of a layer of incompressible viscous fluid lying above a rigid plane and with an upper boundary given by a free surface. The fluid is subject to a constant external force with a horizontal component, which arises in modeling the motion of such a fluid down an inclined plane, after a coordinate change. We consider the problem both with and without surface tension for horizontally periodic flows. This problem gives rise to shear-flow equilibrium solutions, and the main thrust of this paper is to study the asymptotic stability of the equilibria in certain parameter regimes. We prove that there exists a parameter regime in which sufficiently small perturbations of the equilibrium at time t = 0 give rise to global-in-time solutions that return to equilibrium exponentially in the case with surface tension and almost exponentially in the case without surface tension. We also establish a vanishing surface tension limit, which connects the solutions with and without surface tension.2010 Mathematics Subject Classification. Primary: 35Q30, 35R35, 76E17; Secondary: 35B40, 76D45, 76E05 .

show abstract

“…Suppose that (v, q, ζ) solve (3.1), where Φ, A, J, etc are determined by η as in (1. 19) and (1.21). Then…”

Section: Evolution Of the Energy And Dissipationmentioning

confidence: 96%

Section: Eulerian Perturbationmentioning

confidence: 99%

Asymptotic stability of shear-flow solutions to incompressible viscous free boundary problems with and without surface tension

Tice

2018

Z. Angew. Math. Phys.

View full text Add to dashboard Cite

show abstract

On a linearized system arising in the study of viscous surface flow down an inclined plane

Cited by 1 publication

References 7 publications

Asymptotic stability of shear-flow solutions to incompressible viscous free boundary problems with and without surface tension

Asymptotic stability of shear-flow solutions to incompressible viscous free boundary problems with and without surface tension

Contact Info

Product

Resources

About