Related papers: Singularly Perturbed Gradient Flows and Evolution …
We investigate here linear stability in a canonical three-dimensional boundary layer generated by the superposition of a spanwise pressure gradient upon an otherwise standard channel flow. As the main result, we introduce a simple…
In the context of cell motility modelling and more particularly related to the Filament Based Lamelipodium Model [Manhart et al 2015 & 2017], this work deals with a rigorous mathematical proof of convergence between solutions of two…
The paper presents numerical methods for unsteady flows of a viscous incompressible fluid in internal domains with many inlet/outlet sections. The novel variants of dissipative boundary conditions augmented by the inertia terms are used at…
Quasistatic evolutions of critical points of time-dependent energies exhibit piecewise smooth behavior, making them useful for modeling continuum mechanics phenomena like elastic-plasticity and fracture. Traditionally, such evolutions have…
Vortices are topological defects associated with superfluids and superconductors, which, when mobile, dissipate energy destroying the dissipation-less nature of the superfluid. The nature of this "quantum dissipation" is rooted in the…
High-pressure transcritical fluid flows are central to modern energy and propulsion systems. A key challenge arises in confined configurations, where optimizing performance requires a detailed understanding of the coupled hydrodynamic and…
Prediction of flow to boreholes or excavations in fractured low-permeability rocks is important for resource extraction and disposal or sequestration activities. Analytical solutions for fluid pressure and flowrate, when available, are…
Motivated by a constrained minimization problem, it is studied the gradient flows with respect to Hessian Riemannian metrics induced by convex functions of Legendre type. The first result characterizes Hessian Riemannian structures on…
We study the existence and long-time asymptotics of weak solutions to a system of two nonlinear drift-diffusion equations that has a gradient flow structure in the Wasserstein distance. The two equations are coupled through a…
The weakly compressible methods to simulate incompressible flows are in a state of rapid development, owing to the envisaged efficiency they offer for parallel computing. The pressure waves in such methods travel at finite speeds, and hence…
McDonald and Clerk [Phys.\ Rev.\ Research 5, 033107 (2023)] showed that for linear open quantum systems the Liouvillian spectrum is independent of the noise strength. We first make this noise-independence principle precise in continuous…
This is the second in a series of papers where we analyze the incompressible Navier-Stokes equations in H\"older spaces. We obtain, to our knowledge, the very first genuinely super-critical regularity criterion for this system of equations…
This paper is devoted to existence and uniqueness results for classes of nonlinear diffusion equations (or systems) which may be viewed as regular perturbations of Wasserstein gradient flows. First, in the case. where the drift is a…
We prove that viscosity solutions of geometric equations in step two Carnot groups can be equivalently reformulated by restricting the set of test functions at the singular points. These are characteristic points for the level sets of the…
The Sierpinski gasket is known to support an exotic stochastic process called the asymptotically one-dimensional diffusion. This process displays local anisotropy, as there is a preferred direction of motion which dominates at the…
This paper concerns a new class of discontinuous dynamical systems for constrained optimization. These dynamics are particularly suited to solve nonlinear, non-convex problems in closed-loop with a physical system. Such approaches using…
The aim of this article is to construct solutions to second order in time stochastic partial differential equations and to show hypocoercivity of the corresponding transition semigroups. More generally, we analyze non-linear…
We consider a diffuse-interface model for two-phase incompressible viscous flows with a soluble surfactant in a bounded porous medium. This hydrodynamic system consists of a Darcy--Forchheimer equation for the seepage velocity…
We analyse numerical errors (dissipation and dispersion) introduced by the discretisation of inviscid and viscous terms in energy stable discontinuous Galerkin methods. First, we analyse these methods using a linear von Neumann analysis…
We show, for mean curvature flows in Euclidean space, that if one of the tangent flows at a given space-time point consists of a closed, multiplicity-one, smoothly embedded self-similar shrinker, then it is the unique tangent flow at that…