On the Helicity conservation for the incompressible Euler equations

2018/12/03 by De Rosa, Luigi · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1812.00678

Abstract

In this work we investigate the helicity regularity for weak solutions of the incompressible Euler equations. To prove regularity and conservation of the helicity we will threat the velocity u and its curl u as two independent functions and we mainly show that the helicity is a constant of motion assuming u ∈ L^2r_t(C^θ_x) and curl u ∈ L^κ_t(W^α,1_x) where r,κ are conjugate Hölder exponents and 2θ+α≥ 1. Using the same techniques we also show that the helicity has a suitable Hölder regularity even in the range where it is not necessarily constant.

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