Dissipative continuous Euler flows
Camillo De Lellis, L\'aszl\'o Sz\'ekelyhidi Jr
TL;DR
This paper demonstrates the existence of continuous, periodic solutions to the 3D incompressible Euler equations that dissipate total kinetic energy, challenging traditional conservation expectations.
Contribution
It introduces the first known examples of dissipative continuous Euler flows, expanding understanding of energy behavior in ideal fluid dynamics.
Findings
Existence of dissipative continuous solutions to 3D Euler equations
Solutions are periodic in time and space
Energy dissipation occurs despite ideal fluid assumptions
Abstract
We show the existence of continuous periodic solutions of the 3D incompressible Euler equations which dissipate the total kinetic energy.
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