C0+ Convex Integration Scheme for the Euler Equations

Didmishe, Rohan (2025) C0+ Convex Integration Scheme for the Euler Equations. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Rohan Didmishe (20MS224)) 20MS224_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (1MB)

Abstract

This is a thesis project exploring how to construct exact weak solutions of the Euler Equations using a convex integration scheme which is implemented in the review article of Prof. Buckmaster and Prof. Vicol (1). These solutions lie in a H¨older class with a small exponent β ≪ 1 3 and are trying to emulate features of turbulent flows that Kolmogorov and Onsager had discussed in the 1900s. First a brief introduction is given to the history and physical relevance of both the Euler equations and the Onsager Theorem. Then giving an outline, later we prove a version of the theorem using the scheme from the same article. Proofs of lemmas are given in detail and the intuitive ideas are also presented as explicitly as possible. The limitations and possible fixes are also mentioned in the end.

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