相关论文: Gradient flows without blow-up for Lefschetz thimb…
In [8], the gradient conjecture of R. Thom was proven for gradient flows of analytic functions on Rn. This result means that the secant at a limit point converges, so that the flow cannot spiral forever. Once the trajectory becomes…
It is known that there is a class of semilinear parabolic equations for which interior gradient blow-up (in finite time) occurs for some solutions. We construct a continuation of such solutions after gradient blow-up. This continuation is…
This thesis analyze the Wasserstein gradient flow of a functional defined as a double convolution of a non-smooth repulsive interaction potential. To be more precise, the potential under investigation has a -|x| behavior close to the…
In this paper we provide a variational characterisation for a class of non-linear evolution equations with constant non-negative Dirichlet boundary conditions on a bounded domain as gradient flows in the space of non-negative measures. The…
When addressing ordinary differential equations in infinite dimensional Banach spaces, an interesting question that arises concerns the existence (or non existence) of blowing up solutions in finite time. In this manuscript we discuss this…
We develop a lattice Boltzmann (LB) model for immiscible two-phase flow simulations with central moments (CMs). This successfully combines a three-dimensional nonorthogonal CM-based LB scheme [A. De Rosis, Phys. Rev. E 95, 013310 (2017)]…
We concider, the blow-up solutions for a coupled reaction diffusion system with gradient terms. The main purpose is to understand whether the gradient terms effect the blow-up properties. We derive the upper and lower blow-up rate estimates…
In this article, we study the blowup phenomena of compressible Euler equations with non-vacuum initial data. Our new results, which cover a general class of testing functions, present new initial value blowup conditions. The corresponding…
We consider the initial-boundary value problem of a simplified nematic liquid crystal flow in a bounded, smooth domain $\Omega \subset \mathbb R^2$. Given any $k$ distinct points in the domain, we develop a new {\em inner--outer gluing…
The gradient scheme framework is based on a small number of properties and encompasses a large number of numerical methods for diffusion models. We recall these properties and develop some new generic tools associated with the gradient…
The dynamics of gradient and Hamiltonian flows with particular application to flows on adjoint orbits of a Lie group and the extension of this setting to flows on a loop group are discussed. Different types of gradient flows that arise from…
In this paper, we study two kind of L^2 norm preserved non-local heat flows on closed manifolds. We first study the global existence, stability and asymptotic behavior to such non-local heat flows. Next we give the gradient estimates of…
In a recent paper [F. Vega Reyes et al., Phys. Rev. Lett. 104, 028001 (2010)] we presented a preliminary description of a special class of steady Couette flows in dilute granular gases. In all flows of this class the viscous heating is…
We show for the first time that sustained turbulence is possible at low magnetic Prandtl number for Keplerian flows with no mean magnetic flux. Our results indicate that increasing the vertical domain size is equivalent to increasing the…
In this paper, we study inextensible flows of non-null curves in E^n,1. We give necessary and sufficient conditions for inextensible flow of nonnull curves in E^n,1.
We study the deformation and dynamics of droplets in time-dependent flows using 3D numerical simulations of two immiscible fluids based on the lattice Boltzmann model (LBM). Analytical models are available in the literature, which assume…
Wasserstein gradient flows on probability measures have found a host of applications in various optimization problems. They typically arise as the continuum limit of exchangeable particle systems evolving by some mean-field interaction…
A multi-scale model for the evolution of the velocity gradient tensor in fully developed turbulence is proposed. The model is based on a coupling between a ``Restricted Euler'' dynamics [{\it P. Vieillefosse, Physica A, {\bf 14}, 150…
The 2d Boussinesq equations model large scale atmospheric and oceanic flows. Whether its solutions develop a singularity in finite-time remains a classical open problem in mathematical fluid dynamics. In this work, blowup from smooth…
We consider gradient flows of surface energies which depend on the surface by a parameterization and on a tangential tensor field. The flow allows for dissipation by evolving the parameterization and the tensor field simultaneously. This…