Related papers: Neutrally floating objects of density 1/2 in three…

We prove that the 3-D free-surface incompressible Euler equations with regular initial geometries and velocity fields have solutions which can form a finite-time "splash" (or "splat") singularity first introduced in [9], wherein the…

We investigate a duality relation between floating and illumination bodies. The definitions of these two bodies suggest that the polar of the floating body should be similar to the illumination body of the polar. We consider this question…

Motivated by the study of uniaxial crystal optics, we consider a coupled system of $3D$ anisotropic wave equations, in which they have the same speed only in one direction but distinct speeds in the other directions. Moreover, this system…

We consider the classical compressible Euler's Equations in three space dimensions with an arbitrary equation of state, and whose initial data corresponds to a constant state outside a sphere. Under suitable restriction on the size of the…

This paper investigates the Newton's problem of minimal resistance for a body moving through a fluid whose density decreases exponentially with altitude. We prove the local existence and regularity of radial solutions $u(r)$ satisfying the…

We investigate the properties of a special class of singular solutions for a self-gravitating perfect fluid in general relativity: the singular isothermal sphere. For arbitrary constant equation-of-state parameter $w=p/\rho$, there exist…

Following Lortz, we construct a family of smooth steady states of the ideal, incompressible Euler equation in three dimensions that possess no continuous Euclidean symmetry. As in Lortz, they do possess a planar reflection symmetry and, as…

This paper investigates solitary water waves propagating along the surface of a two-dimensional dielectric fluid with constant vorticity in the presence of an external electric field. We formulate the system as a nonlinear free boundary…

We study some properties of static spherically symmetric elastic bodies in general relativity using both analytical and numerical tools. The materials considered belong to the class of John elastic materials and reduce to perfect fluids…

We discuss different equilibrium problems for hyperelastic solids immersed in a fluid at rest. In particular, solids are subjected to gravity and hydrostatic pressure on their immersed boundaries. By means of a variational approach, we…

We examine the equilibrium configurations of a nematic liquid crystal with an immersed body in two-dimensions. A complex variables formulation provides a means for finding analytical solutions in the case of strong anchoring. Local…

The transport of slightly deformable chiral objects in a uniform shear flow is investigated. Depending on the equilibrium configuration one finds up to four different asymptotic states that can be distinguished by a lateral drift velocity…

We consider the two-dimensional water wave problem in the case where the free interface of the fluid meets a vertical wall at a possibly non-right angle; and where the free interface can be non-$C^1$ with angled crests. We assume that the…

The relative equilibria for the spherical, finite density 3 body problem are identified. Specifically, there are 28 distinct relative equilibria in this problem which include the classical 5 relative equilibria for the point-mass 3-body…

Whether singularities can form in fluids remains a foundational unanswered question in mathematics. This phenomenon occurs when solutions to governing equations, such as the 3D Euler equations, develop infinite gradients from smooth initial…

We study the equilibrium configurations of a possibly asymmetric fluid-structure-interaction problem. The fluid is confined in a bounded planar channel and is governed by the stationary Navier-Stokes equations with laminar inflow and…

We consider the evolution of a small rigid body in an incompressible viscous fluid filling the whole space $\rline^3$. When the small rigid body shrinks to a "massless" point in the sense that its density is constant, we prove that the…

The equations in conservative form for nonlinear waves modeling on a liquid film flowing down a vertical plane have been investigated. It has been found that in the computational domain extended along the transverse axis the equations with…

In this paper, we study the steady solutions of Euler-Poisson equations in bounded domains with prescribed angular velocity. This models a rotating Newtonian star consisting of a compressible perfect fluid with given equation of state…

In this paper we study the interaction of a small rigid body in a viscous compressible fluid. The system occupies a bounded three dimensional domain. The object it allowed to freely move and its dynamics follows the Newton's laws. We show…