The first half of Onsager's conjecture states that the Euler equations of an ideal
incompressible fluid conserve energy if u (⋅, t)∈ C 0, θ (T 3) with θ> 1 3. In this paper, we …

The goal of this note is to show that, in a bounded domain Ω ⊂ R^ n Ω⊂ R n, with ∂ Ω ∈
C^ 2∂ Ω∈ C 2, any weak solution (u (x, t), p (x, t))(u (x, t), p (x, t)), of the Euler equations of …

We consider the incompressible Euler equations in a bounded domain in three space
dimensions. Recently, the first two authors proved Onsager's conjecture for bounded …

We show that weak solutions of general conservation laws in bounded domains conserve
their generalized entropy, and other respective companion laws, if they possess a certain …

We consider the compressible isentropic Euler equations on [0, T]× 𝕋 d with a pressure law
p∈ C 1, γ− 1, where 1≤ γ< 2. This includes all physically relevant cases, eg, the …

The non-local degenerate Cahn–Hilliard equation is derived from the Vlasov equation with
long range attraction. We study the local limit as the delocalization parameter converges to …

The aim of this work is to extend and prove the Onsager conjecture for a class of
conservation laws that possess generalized entropy. One of the main findings of this work is …

We consider the motion of an inviscid compressible fluid under the mutual interactions with
magnetic field. We show that the initial value problem is ill-posed in the class of weak …

In this paper, we derive a sufficient condition kee** energy conservation in terms of the
gradient of the velocity for the weak solutions of the compressible Euler equations for both …

In this article we study the principle of energy conservation for the Euler–Korteweg system.
We formulate an Onsager-type sufficient regularity condition for weak solutions of the Euler …