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We study the limiting behavior of viscous incompressible flows when the fluid domain is allowed to expand as the viscosity vanishes. We describe precise conditions under which the limiting flow satisfies the full space Euler equations. The…
We consider the incompressible Euler and Navier-Stokes equations in a three-dimensional moving thin domain. Under the assumption that the moving thin domain degenerates into a two-dimensional moving closed surface as the width of the thin…
Hypothesis: Droplet coalescence process is important in many applications and has been studied extensively when two droplets are surrounded by gas. However, the coalescence dynamics would be different when the two droplets are surrounded by…
A circular twist disclination is a nontrivial example of a defect in an elastic continuum that causes large deformations. The minimal potential energy and the corresponding displacement field is calculated by solving the…
We consider the physical setup of a three-dimensional fluid-structure interaction problem. A viscous compressible gas or liquid interacts with a nonlinear, visco-elastic, three-dimensional bulk solid. The latter is described by a hyperbolic…
This letter presents a theory on the coalescence of two spherical liquid droplets that are initially stationary. The evolution of the radius of a liquid neck formed upon coalescence was formulated as an initial value problem and then solved…
In this paper, we investigate the Dirichlet problem on lower dimensional manifolds for a class of weighted elliptic equations with coefficients that are singular on such sets. Specifically, we study the problem \[\begin{cases} -{\rm…
It is known that the overlap of two energy eigenstates in a decaying quantum system is bounded from above by a function of the energy detuning and the individual decay rates. This is usually traced back to the positive definiteness of an…
The notion of singular limiting induced from continuum solutions (slic-solutions) is applied to the problem of cavitation in nonlinear elasticity, in order to re-assess an example of non-uniqueness of entropic weak solutions (with…
Two-dimensional arrays of nonlinear electric oscillators are considered theoretically, where nearest neighbors are coupled by relatively small, constant, but non-equal capacitors. The dynamics is approximately reduced to a weakly…
We consider both divergence and non-divergence parabolic equations on a half space in weighted Sobolev spaces. All the leading coefficients are assumed to be only measurable in the time and one spatial variable except one coefficient, which…
It has been found in numerical experiments that when one removes a sector from an elastic sheet and glues the edges of the sector back together, the resulting configuration is radially symmetric and nearly conical. We make a rigorous…
The free energy of a crystalline domain coexisting with a liquid phase on a spherical vesicle may be approximated by an elastic or stretching energy and a line tension term. The stretching energy generally grows as the area of the domain,…
This paper investigates the local existence and uniqueness of strong solutions to the three-dimensional compressible Navier-Stokes equations with density-dependent viscosities in exterior domains. When both the shear and bulk viscosity…
We consider the inertial motion of a system constituted by a rigid body with an interior cavity entirely filled with a viscous incompressible fluid. Navier boundary conditions are imposed on the cavity surface. We prove the existence of…
The main goal of this work is to clarify and quantify, by means of mathematical analysis, the role of structural viscoelasticity in the biomechanical response of deformable porous media with incompressible constituents to sudden changes in…
We consider two-dimensional hydroelastic waves, in which a free fluid surface separates two fluids of infinite vertical extent. Elastic effects are accounted for at the interface, with a parameter measuring the elastic bending force and…
Unit-vector fields $\nvec$ on a convex polyhedron $P$ subject to tangent boundary conditions provide a simple model of nematic liquid crystals in prototype bistable displays. The equilibrium and metastable configurations correspond to…
This paper studies the inviscid limit of the two-dimensional incompressible viscoelasticity, which is a system coupling a Navier-Stokes equation with a transport equation for the deformation tensor. The existence of global smooth solutions…
Amorphous solids are known to fail catastrophically and in some situations, nano-scaled cavities are believed to play a significant role in the failure. In a recent work, using numerical simulations, we have shown the correspondence between…