Computational Convex Integration

Convex integration (CI) has been developed in the past 10 years as a constructive technique for the incompressible Euler equations in connection with Onsager’s conjecture. The goal of this project is to transform the theoretical CI algorithm into a computational algorithm, enabling us for the first time to directly compute weak solutions of the Euler equations with small-scale structure compatible with Kolmogorov’s K41 theory and whose existence has been first conjectured by L. Onsager in 1949. More specifically, our aim is to 

  • develop a numerical implementation of the construction of weak solutions with the ability to go beyond temporal scales currently available in HPC turbulence simulations.
  • compare numerical convergence rates to available theoretical bounds.
  • study for the first time Lagrangian properties of K41 and intermittent weak solutions.
  • explore the numerical construction of weak solutions with multifractal properties, with an eye towards new, HPC-informed bounds on structure function exponents.

The project requires both theoretical and computational expertise.

Principal investigators

Prof. Dr.-Ing. Rupert Klein

Freie Universität Berlin
Department of Mathematics and Computer Science
Geophysical Fluid Dynamics

rupert.klein@we dont want


Ruppert Klein

Dr. habil. Peter Korn

Max-Planck-Institut für Meteorologie
Applied Mathematics and Computational Physics

peter.korn@we dont want


Peter Korn

Prof. Dr. László Székelyhidi

Max-Planck-Institut für Mathematik in den Naturwissenschaften
Applied Analysis Group

laszlo.szekelyhidi@we dont want


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