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On the Convergence of the Spectral Viscosity Method for the Two-Dimensional Incompressible Euler Equations with Rough Initial Data

  • Samuel LanthalerEmail author
  • Siddhartha Mishra
Article
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Abstract

We propose a spectral viscosity method to approximate the two-dimensional Euler equations with rough initial data and prove that the method converges to a weak solution for a large class of initial data, including when the initial vorticity is in the so-called Delort class, i.e., it is a sum of a signed measure and an integrable function. This provides the first convergence proof for a numerical method approximating the Euler equations with such rough initial data and closes the gap between the available existence theory and rigorous convergence results for numerical methods. We also present numerical experiments, including computations of vortex sheets and confined eddies, to illustrate the proposed method.

Keywords

Incompressible Euler Spectral viscosity Vortex sheet Convergence Compensated compactness 

Mathematics Subject Classification

65M12 65M70 

Notes

Acknowledgements

The research of SL and SM is partially supported by the European Research Council (ERC) consolidator Grant ERC COG 770880: COMANFLO.

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Copyright information

© SFoCM 2019

Authors and Affiliations

  1. 1.Seminar for Applied Mathematics, Department of MathematicsETH ZurichZurichSwitzerland

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