相关论文: The binormal flow with initial data being polygona…

In this article we consider the initial value problem of the binormal flow with initial data given by curves that are regular except at one point where they have a corner. We prove that under suitable conditions on the initial data a unique…

The aim of this paper is threefold. First we display solutions of the cubic nonlinear Schr{\"o}dinger equation on R in link with initial data a sum of Dirac masses. Secondly we show a Talbot effect for the same equation. Finally we prove…

We extend the inverse spectral transform for the conservative Camassa-Holm flow on the line to a class of initial data that requires strong decay at one endpoint but only mild boundedness-type conditions at the other endpoint. The latter…

It is shown how the initial azimuthally asymmetric flow develops from the free-streaming + sudden equilibration approximation to the early dynamics in relativistic heavy-ion collisions. Consequences for the hydrodynamics and physical…

The proof given in the paper was incomplete due to an omission in the proof of Lemma 2. A corrected and improved version of the paper is in arXiv:0902.2486.

We investigate the combinatorial Ricci flow on a surface of nonpositive Euler characteristic when the necessary and sufficient condition for the convergence of the combinatorial Ricci flow is not valid. This observation addresses one of…

Normalizing flows have been successfully modeling a complex probability distribution as an invertible transformation of a simple base distribution. However, there are often applications that require more than invertibility. For instance,…

If we want to deform a compact Riemannian manifold with boundary using Ricci flow, we first need to decide on appropriate boundary conditions. We would like these conditions to reflect the geometric nature of the flow and allow for a…

We investigate the issue of uniqueness of the limit flow for a relevant class of quasi-linear parabolic equations defined on the whole space. More precisely, we shall investigate conditions which guarantee that the global solutions decay at…

The mathematical properties of a nonlinear parabolic equation arising in the modelling of non-newtonian flows are investigated. The peculiarity of this equation is that it may degenerate into a hyperbolic equation (in fact a linear…

We study doubly nonlinear parabolic equation arising from the gradient flow for p-Sobolev type inequality, referred as p-Sobolev flow from now on, which includes the classical Yamabe flow on a bounded domain in Euclidean space in the…

The binormal flow is a model for the dynamics of a vortex filament in a 3-D inviscid incompressible fluid. The flow is also related with the classical continuous Heisenberg model in ferromagnetism, and the 1-D cubic Schr\"odinger equation.…

In the last three decades there has been an intense activity on the exploration of turbulent phenomena of dispersive equations, as for instance the growth of Sobolev norms since the work of Bourgain in the 90s. In general the 1D cubic…

This thesis presents an overview of the flow equations recently introduced by Wegner. The little known mathematical framework of the flow in the manifold of unitarily equivalent matrices, as discovered in the mathematical literature before…

It is presently believed that flows of viscoelastic polymer solutions in geometries such as a straight pipe or channel are linearly stable. Here we present experimental evidence that such flows can be nonlinearly unstable and can exhibit a…

We propose a weak formulation for the binormal curvature flow of curves in $\R^3.$ This formulation is sufficiently broad to consider integral currents as initial data, and sufficiently strong for the weak-strong uniqueness property to…

We analyse second order (in Riemann curvature) geometric flows (un-normalised) on locally homogeneous three manifolds and look for specific features through the solutions (analytic whereever possible, otherwise numerical) of the evolution…

We study the flow equation for the $\mathcal{N}=1$ supersymmetric $O(N)$ nonlinear sigma model in two dimensions, which cannot be given by the gradient of the action, as evident from dimensional analysis. Imposing the condition on the flow…

Consider a fluid flowing through a junction between two pipes with different sections. Its evolution is described by the 2D or 3D Euler equations, whose analytical theory is far from complete and whose numerical treatment may be rather…

We review some recent results concerning the evolution of a vortex filament and its relation to the cubic non-linear Schr\"odinger equation. Selfsimilar solutions and questions related to their stability are studied.