Publication

Instability and Non uniqueness for the Euler and Navier–Stokes Equations

2026

Abstract

In the last 20 years, there has been remarkable progress in understanding nonuniqueness of solutions to the fundamental partial differential equations of incompressible fluid dynamics, namely the Euler and Navier–Stokes equations. They stem from different viewpoints: just to mention a few, they include convex integration, instability in self-similar variables, and numerical evidences. The talk will provide an overview of these developments, focusing on our current understanding of the linear instability of the equations in connection with their nonuniqueness.

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2026

Abstract

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Related concepts (32)

Navier–Stokes equations

The Navier–Stokes equations (nævˈjeː_stəʊks ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842-1850 (Stokes). The Navier–Stokes equations mathematically express momentum balance and conservation of mass for Newtonian fluids.

Differential equation

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.

Fluid dynamics

In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation.

Related publications (32)

Instability and Non uniqueness for the Euler and Navier–Stokes Equations

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