Related papers: An analytic study of bi-harmonic flow with a forci…
In this paper, we consider incompressible Euler flows in $ \mathbb{R}^{4} $ under bi-rotational symmetry, namely solutions that are invariant under rotations in $\mathbb{R}^{4}$ fixing either the first two or last two axes. With the…
In this paper, we study flexibility of weak solutions to the Monge-Amp\`ere system (MA) via convex integration. This new system of Pdes is an extension of the Monge-Amp\`ere equation in $d=2$ dimensions, naturally arising from the…
In this paper we study the $L^2$-gradient flow of the penalized elastic energy on networks of $q$-curves in $\R^{n}$ for $q \geq 3$. Each curve is fixed at one end-point and at the other is joint to the other curves at a movable…
In the first half of the paper we construct a Morse-type theory on certain spaces of braid diagrams. We define a topological invariant of closed positive braids which is correlated with the existence of invariant sets of parabolic flows…
In the finite element analysis with fast decoupled time integration scheme for viscoelastic fluid (the Leonov model) flow, we investigate strong nonlinear behavior in 2D creeping contraction flow. The algorithm is applicable in the whole…
This paper concerns the evolution of a closed hypersurface of dimension $n(\geq 2)$ in the Euclidean space ${\mathbb{R}}^{n+1}$ under a mixed volume preserving flow. The speed equals a power $\beta (\geq 1)$ of homogeneous, either convex or…
In this paper, we study the two-dimensional steady compactly supported incompressible Euler equations with free boundaries. We consider flows with constant vorticity that are perturbations of annular equilibria, in contrast to the laminar…
The stability of two-dimensional Poiseuille flow and plane Couette flow for concentrated suspensions is investigated. Linear stability analysis of the two-phase flow model for both flow geometries shows the existence of a convectively…
We are concerned with a system of partial differential equations describing internal flows of homogeneous incompressible fluids of Bingham type in which the value of activation (the so-called yield) stress depends on the internal pore…
In this article we study Chen's flow of curves from theoreical and numerical perspectives. We investigate two settings: that of closed immersed $\omega$-circles, and immersed lines satisfying a cocompactness condition. In each of the…
Inspired by the all-important conformal invariance of harmonic maps on two-dimensional domains, this article studies the relationship between biharmonicity and conformality. We first give a characterization of biharmonic morphisms,…
Travelling and rotating waves are ubiquitous phenomena observed in time dependent PDEs modelling the combined effect of dissipation and non-linear interaction. From an abstract viewpoint they appear as relative equilibria of an equivariant…
Depth averaged conservation equations are written for granular surface flows. Their application to the study of steady surface flows in a rotating drum allows to find experimentally the constitutive relations needed to close these equations…
We introduce a novel energy method that reinterprets ``curve shortening'' as ``tangent aligning''. This conceptual shift enables the variational study of infinite-length curves evolving by the curve shortening flow, as well as higher order…
This article studies special solutions to symplectic curvature flow in dimension four. Firstly, we derive a local normal form for static solutions in terms of holomorphic data and use this normal form to show that every complete static…
Many large-scale and distributed optimization problems can be brought into a composite form in which the objective function is given by the sum of a smooth term and a nonsmooth regularizer. Such problems can be solved via a proximal…
This paper concerns the inverse mean curvature flow of convex hypersurfaces which are Lipschitz in general. After defining a weak solution, we study the evolution of the singularity by looking at the blow-up tangent cone around each…
In this article we study the asymptotic behavior of incompressible, ideal, time-dependent two dimensional flow in the exterior of a single smooth obstacle when the size of the obstacle becomes very small. Our main purpose is to identify the…
We consider the parabolic polyharmonic diffusion and $L^2$-gradient flows of the $m$-th arclength derivative of curvature for regular closed curves evolving with generalised Neumann boundary conditions. In the polyharmonic case, we prove…
Parametric finite element discretizations of constrained geometric flows must simultaneously address high-order geometric stiffness, mesh degeneration, and nonlinear global constraints. This paper develops a stabilized dual-SAV (scalar…