Dissipative continuous Euler flows
- 1.5k Downloads
We show the existence of continuous periodic solutions of the 3D incompressible Euler equations which dissipate the total kinetic energy.
KeywordsEuler Equation Reynolds Stress Continuous Solution Total Kinetic Energy Isometric Embedding
We wish to thank Peter Constantin and Sergio Conti for several very valuable discussions on earlier attempts to prove Theorem 1.1. Moreover we are grateful to Antoine Choffrut for several comments on earlier versions of the paper, which considerably improved its readability. The first author acknowledges the support of the SFB Grant TR71, the second author acknowledges the support of the ERC Grant Agreement No. 277993 and the support of the Hausdorff Center for Mathematics in Bonn.
- 1.Chiodaroli, E.: A counterexample to well-posedness of entropy solutions to the incompressible Euler system. Preprint (2012) Google Scholar
- 8.De Lellis, C., Székelyhidi, L. Jr.: The h-principle and the equations of fluid dynamics. Preprint (2011) Google Scholar
- 10.Eliashberg, Y., Mishachev, N.: Introduction to the h-principle. Graduate Studies in Mathematics, vol. 48. American Mathematical Society, Providence (2002) Google Scholar
- 27.Székelyhidi, L. Jr., Wiedemann, E.: Young measures generated by ideal incompressible fluid flows. doi: 10.1007/s00205-012-0540-5