Publication

Flexibility of two-dimensional Euler flows with integrable vorticity

2026

Abstract

We propose a new convex integration scheme in fluid mechanics, and we provide an application to the two-dimensional Euler equations. We prove the flexibility and nonuniqueness of L∞L2 weak solutions with vorticity in L∞Lp for some p>1, surpassing for the first time the critical scaling of the standard convex integration technique. To achieve this, we introduce several new ideas, including: a new family of building blocks built from the Lamb–Chaplygin dipole; a new method to cancel the error based on time averages and nonperiodic, spatially anisotropic perturbations.

Official source

Graph Chat

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.

2026

Abstract

Official source

Related concepts (32)

Euler equations (fluid dynamics)

In fluid dynamics, the Euler equations are a set of quasilinear partial differential equations governing adiabatic and inviscid flow. They are named after Leonhard Euler. In particular, they correspond to the Navier–Stokes equations with zero viscosity and zero thermal conductivity. The Euler equations can be applied to incompressible or compressible flow. The incompressible Euler equations consist of Cauchy equations for conservation of mass and balance of momentum, together with the incompressibility condition that the flow velocity is a solenoidal field.

Fluid mechanics

Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical, and biomedical engineering, as well as geophysics, oceanography, meteorology, astrophysics, and biology. It can be divided into fluid statics, the study of fluids at rest; and fluid dynamics, the study of the effect of forces on fluid motion.

Critical phenomena

In physics, critical phenomena is the collective name associated with the physics of critical points. Most of them stem from the divergence of the correlation length, but also the dynamics slows down. Critical phenomena include scaling relations among different quantities, power-law divergences of some quantities (such as the magnetic susceptibility in the ferromagnetic phase transition) described by critical exponents, universality, fractal behaviour, and ergodicity breaking.

Related publications (4)

Flexibility of two-dimensional Euler flows with integrable vorticity

Chat with Graph Search

On the role of poroelasticity in the near-tip region of a hydraulic fracture

Isogeometric numerical simulation of solute dynamics in blood flows

Calculation of variable-topology free surface flows using CONNFFESSIT