Related papers: Local smoothing effects for the water-wave problem…

In this paper we prove the local well-posedness (LWP) for the 3D compressible Euler equations describing the motion of a liquid in an unbounded initial domain with moving boundary. The liquid is under the influence of gravity but without…

The dynamics of surface waves traveling along the boundary of a liquid medium are changed by the presence of floating plates and membranes, contributing to a number of important phenomena in a wide range of applications. Mathematically, if…

In this paper, we study the flow physics underlying the recently developed remote sensing capability of detecting oceanic microplastics, which is based on the measurable surface roughness reduction induced by the presence of microplastics…

We consider the free boundary problem for a layer of viscous, incompressible fluid in a uniform gravitational field, lying above a rigid bottom and below the atmosphere. For the "semi-small" initial data, we prove the zero surface tension…

This paper is concerned with the study of the wave equation on compact surfaces and locally distributed damping. We study the case where the damping is effective on the complement of visible umbilical sets.

We consider the sloshing problem for an incompressible, inviscid, irrotational fluid in an open container, including effects due to surface tension on the free surface. We restrict ourselves to a constant contact angle and seek…

We briefly review the effects of selective solvation of ions in aqueous mixtures, where the ion densities and the composition fluctuations are strongly coupled. We then examine the surface tension \gamma of a liquid-liquid interface in the…

This paper is concerned with the study of the wave equation on compact surfaces and locally distributed damping. We study the case where the damping is effective in a well-chosen subset of arbitrarily small measure.

We study the growth of small-scale inhomogeneities of the density of particles floating in weakly nonlinear, small-amplitude, surface waves. Despite the amplitude smallness, the accumulated effect of the long-time evolution may produce…

This paper is withdrawn.

This paper is concerned with the Cauchy problem of the one-dimensional free surface equation of shallow water wave, we obtain local well-posedness of the free surface equation of shallow water wave in Sobolev spaces. In addition, we also…

When a body is exposed to external forces large local stresses may occur at the surface because of surface roughness. Surface stress concentration is important for many applications and in particular for fatigue due to pulsating external…

Robust surfaces capable of reducing flow drag, controlling heat and mass transfer, and resisting fouling in fluid flows are important for various applications. In this context, textured surfaces impregnated with a liquid lubricant show…

This paper contains details of calculation of the surface wave excitation by a fast moving charged particle in a thin uniform metal film surrounded by a dielectic medium. Early on the effect was described in the paper arXiv:0911.0565 03…

We present a systematic, quantitative assessment of the impact of pore size disorder and its interplay with flow rates and wettability on immiscible displacement of a viscous fluid. Pore-scale simulations and micromodel experiments show…

Eshelby's theory of inclusions has wide-reaching implications across the mechanics of materials and structures including the theories of composites, fracture, and plasticity. However, it does not include the effects of surface stress, which…

The purpose of this paper is to improve the known estimates for Mockenhaupt's square function in $\mathbb R^3$ and for Sogge's local smoothing in $\mathbb R^{2+1}$ spacetime. For this we use the trilinear approach of S. Lee and A. Vargas…

Wrinkling of stretched elastic sheets is widely observed, and the scaling relations between the amplitude and wavelength of the wrinkles have been proposed by Cerda and Mahadevan. However, the surface effects should be taken into account…

Using extended Layzer's potential flow model, we investigate the effects of surface tension on the growth of the bubble and spike in combined Rayleigh-Taylor and Kelvin-Helmholtz instability. The nonlinear asymptotic solutions are obtained…

We discuss the microlocal Gevrey smoothing effect for the Schr\"odinger equation with variable coefficients via the propagation property of the wave front set of homogenous type. We apply the microlocal exponential estimates in a Gevrey…