相关论文: Gradient flows without blow-up for Lefschetz thimb…

In this article, we extend Huisken's theorem that convex surfaces flow to round points by mean curvature flow. We construct certain classes of mean convex and non-mean convex hypersurfaces that shrink to round points and use these…

Boltzmann Generators have emerged as a promising machine learning tool for generating samples from equilibrium distributions of molecular systems using Normalizing Flows and importance weighting. Recently, Flow Matching has helped speed up…

Given any continuous, lower bounded and $\kappa$-convex function $V$ on a metric measure space $(X,d,m)$ which is infinitesimally Hilbertian and satisfies some synthetic lower bound for the Ricci curvature in the sense of…

We consider the semilinear heat equation, to which we add a nonlinear gradient term, with a critical power. We construct a solution which blows up in finite time. We also give a sharp description of its blow-up profile. The proof relies on…

We study the possibility of finite-time blow-up for a two dimensional Broadwell model. In a set of rescaled variables, we prove that no self-similar blow-up solution exists, and derive some a priori bounds on the blow-up rate. In the final…

Lattice scales defined using gradient flow are typically very precise, while also easy to calculate. However, different definitions of flows and operators can differ significantly, suggesting possible systematical effects. Using a subset of…

In this paper, the authors consider an initial boundary value problem for the heat flow of equation of surfaces with constant mean curvatures, which was investigated in [On the heat flow of equation of surfaces of constant mean curvatures,…

We study a class of non-linear parabolic systems relevant in turbulence theory. Those systems can be viewed as simplified versions of the Prandtl one-equation and Kolmogorov two-equation models of turbulence. We restrict our attention to…

It is interesting to study the stress concentration between two adjacent stiff inclusions in composite materials, which can be modeled by the Lam\'e system with partially infinite coefficients. To overcome the difficulty from the lack of…

The 2D conservative Boussinesq system describes inviscid, incompressible, buoyant fluid flow in gravity field. The possibility of finite time blow up for solutions of this system is a classical problem of mathematical hydrodynamics. We…

We prove a blow-up criterion in terms of an $L_2$-bound of the curvature for solutions to the curve diffusion flow if the maximal time of existence is finite. In our setting, we consider an evolving family of curves driven by curve…

Luttinger liquid theory of one-dimensional quantum systems ignores exponentially weak backscattering of particles. This endows Luttinger liquids with superfluid properties. The corresponding two-fluid hydrodynamic description available at…

We consider a class of blow-up solutions for perturbed nonlinear heat equations involving gradient terms. We first prove the single point blow-up property for this equation and determine its final blow-up profile. We also give a sharper…

We review the gradient flow for gauge and fermion fields and its applications to lattice gauge theory computations. Using specific examples, we discuss the interplay between perturbative and non-perturbative calculations in the context of…

In linear stability analysis of field quantities described by partial differential equations, the well-established classical theory is all but impossible to apply to concrete problems in its entirety even for uniform backgrounds when the…

In this paper, we develop a scaled gradient-momentum framework for continuous-time optimization that achieves global finite-time convergence. A state-dependent scaling mechanism is introduced to enable classical dynamics, such as…

We analyze the blowup (finite-time singularity) in inviscid shell models of convective turbulence. We show that the blowup exists and its internal structure undergoes a series of bifurcations under a change of shell model parameter. Various…

Flows on surfaces are one of the most fundamental and classical objects in dynamical systems, and are studied from various areas (e.g. integrable systems, differential equations, fluid mechanics). Though hyperbolic flows and recurrent flows…

The previously reported non-equilibrium dissipation law is investigated in turbulent flows generated by various regular and fractal square grids. The flows are documented in terms of various turbulent profiles which reveal their…

The only non-compact linearly stable singularity models for mean curvature flow are cylindrical by Colding-Minicozzi. The uniqueness of blowups at singularities modeled on the cylinders has been established by the same authors. In this…