Typicality results for weak solutions of the incompressible Navier-Stokes equations

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

We consider fluid flows, governed by the Navier-Stokes equations, subject to a steady symmetry-breaking bifurcation and forced by a weak noise acting on a slow timescale. By generalizing the multiple-scale weakly nonlinear expansion technique employed in t ...

The thesis is dedicated to the study of two main partial differential equations (PDEs) in fluid dynamics: the Navier-Stokes equations, which describe the motion of incompressible fluids, and the transport equation with divergence-free velocity fields, whic ...

Weak solutions arise naturally in the study of the Navier-Stokes and Euler equations both from an abstract regularity/blow-up perspective and from physical theories of turbulence. This thesis studies the structure and size of singular set of such weak solu ...

Unstable periodic orbits are believed to underpin the dynamics of turbulence, but by their nature are hard to find computationally. We present a family of methods to converge such unstable periodic orbits for the incompressible Navier-Stokes equations, bas ...

This work is devoted to the study of the main models which describe the motion of incompressible fluids, namely the Navier-Stokes, together with their hypodissipative version, and the Euler equations. We will mainly focus on the analysis of non-smooth weak ...

We are interested in a reduced order method for the efficient simulation of blood flow in arteries. The blood dynamics is modeled by means of the incompressible Navier–Stokes equations. Our algorithm is based on an approximated domain-decomposition of the ...

We consider sample path properties of the solution to the stochastic heat equation, in Rd or bounded domains of Rd, driven by a Levy space-time white noise. When viewed as a stochastic process in time with values in an infinite-dimensional space, the solut ...

Preferential deposition of snow and dust over complex terrain is responsible for a wide range of environmental processes and accounts for a significant source of uncertainty in the surface mass balances of cold and arid regions. Despite the growing body of ...

In this paper we propose a saddle point approach to solve boundary control problems for the steady Navier-Stokes equations with mixed Dirichlet-Neumann boundary conditions, both in two and three dimensions. We provide a comprehensive theoretical framework ...

Steep mountain streams exhibit shallow waters with roughness elements such as stones and pebbles that are comparable in size to flow depth. Owing to the difficulty in measuring fluid velocities at the interface, i.e., from the rough permeable bed to the fr ...

We consider the stationary flow of an inviscid and incompressible fluid of constant density in the region D = (0, L) x R-2. We are concerned with flows that are periodic in the second and third variables and that have prescribed flux through each point of ...

In this paper we propose a method for the strong imposition of random Dirichlet boundary conditions in the Dynamical Low Rank (DLR) approximation of parabolic PDEs and, in particular, incompressible Navier Stokes equations. We show that the DLR variational ...

Motivated by the dynamics of microbubbles near catalytic surfaces in bubble-powered microrockets, we consider theoretically the growth of a free spherical bubble near a flat no-slip surface in a Stokes flow. The flow at the bubble surface is characterised ...

A boundary-fitted moving mesh scheme is presented for the simulation of two-phase flow in two-dimensional and axisymmetric geometries. The incompressible Navier-Stokes equations are solved using the finite element method, and the mini element is used to sa ...

We study the system of linear partial differential equations given by dw + a Lambda w = f, on open subsets of R-n, together with the algebraic equation da Lambda u = beta, where a is a given 1-form, f is a given (k + 1)-form, beta is a given k + 2-form, w ...

We study various aspects of stochastic partial differential equations driven by Lévy white noise. This driving noise, which is a generalization of Gaussian white noise, can be viewed either as a generalized random process or as an independently scattered r ...

Can every measure-valued solution to the compressible Euler equations be approximated by a sequence of weak solutions? We prove that the answer is negative: Generalizing a well-known rigidity result of Ball and James to a more general situation, we constru ...

In this work, we focus on the Dynamical Low Rank (DLR) approximation of PDEs equations with random parameters. This can be interpreted as a reduced basis method, where the approximate solution is expanded in separable form over a set of few deterministic b ...

In this paper we provide a general framework for model reduction methods applied to fluid flow in porous media. Using reduced basis and numerical homogenization techniques we show that the complexity of the numerical approximation of Stokes flow in heterog ...

Fluid flow in porous media is a multiscale process where the effective dynamics, which is often the goal of a computation, depends strongly on the porous micro structure. Resolving the micro structure in the whole porous medium can, however, be prohibitive ...

Typicality results for weak solutions of the incompressible Navier-Stokes equations

Chat with Graph Search

Noise-induced transitions past the onset of a steady symmetry-breaking bifurcation: The case of the sudden expansion

Anomalous dissipation and other non-smooth phenomena in fluids

Blow-up, partial regularity and turbulence in incompressible fluid dynamics

Variational methods for finding periodic orbits in the incompressible Navier Stokes equations

Non-smooth solutions in incompressible fluid dynamics

Model order reduction of flow based on a modular geometrical approximation of blood vessels

Path properties of the solution to the stochastic heat equation with Levy noise

Preferential Deposition of Snow and Dust Over Hills: Governing Processes and Relevant Scales

A saddle point approach to an optimal boundary control problem for steady Navier-Stokes equations

Turbulent Flows over Rough Permeable Beds in Mountain Rivers: Experimental Insights and Modeling

Steady Three-Dimensional Rotational Flows: An Approach Via Two Stream Functions And Nash-Moser Iteration

Dual Dynamically Orthogonal approximation of incompressible Navier Stokes equations with random boundary conditions

Viscous growth and rebound of a bubble near a rigid surface

Interface-fitted moving mesh method for axisymmetric two-phase flow in microchannels

On a generalization of the Poincaré Lemma to equations of the type dw + a ∧ w = f

Stochastic partial differential equations driven by Lévy white noises : generalized random processes, random field solutions and regularity

$A$-free Rigidity and Applications to the Compressible Euler System

Dynamical Low Rank approximation of PDEs with random parameters

Multiscale model reduction methods for flow in heterogeneous porous media

Multiscale methods for Stokes flow in heterogeneous media