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- W4294558052 abstract "Recently the second and third author developed an iterative scheme for obtaining rough solutions of the 3D incompressible Euler equations in Holder spaces (arXiv:1202.1751 and arXiv:1205.3626 (2012)). The motivation comes from Onsager's conjecture. The construction involves a superposition of weakly interacting perturbed Beltrami flows on infinitely many scales. An obstruction to better regularity arises from the errors in the linear transport of a fast periodic flow by a slow velocity field. In a recent paper P. Isett (arXiv:1211.4065) has improved upon our methods, introducing some novel ideas on how to deal with this obstruction, thereby reaching a better Holder exponent - albeit below the one conjectured by Onsager. In this paper we give a shorter proof of Isett's final result, adhering more to the original scheme and introducing some new devices. More precisely we show that for any positive $epsilon$ there exist periodic solutions of the 3D incompressible Euler equations which dissipate the total kinetic energy and belong to the Holder class $C^{frac{1}{5}-epsilon}$." @default.
- W4294558052 created "2022-09-04" @default.
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- W4294558052 date "2013-02-12" @default.
- W4294558052 modified "2023-09-26" @default.
- W4294558052 title "Transporting microstructure and dissipative Euler flows" @default.
- W4294558052 doi "https://doi.org/10.48550/arxiv.1302.2815" @default.
- W4294558052 hasPublicationYear "2013" @default.
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