The L³-based strong Onsager theorem

2023/05/29 by Giri, Vikram, Kwon, Hyunju, Novack, Matthew · 3 citations
#35D30 #35Q31 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2305.18509

Abstract

In this work, we prove the L³-based strong Onsager conjecture for the three-dimensional Euler equations. Our main theorem states that there exist weak solutions which dissipate the total kinetic energy, satisfy the local energy inequality, and belong to C⁰_t (W^{\frac 13-, 3} ∩ L^∞-). More precisely, for every β<\frac 13, we can construct such solutions in the space C⁰_t ( B^β_3,∞ ∩ L^(1)/(1-3β) ).

Cited by

• Dissipative solutions to randomly forced 3D Euler equations
• Fine dissipative properties of Euler solutions with measure first derivatives
• Sharp Non-uniqueness in Law for Stochastic Differential Equations on the Whole Space

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