Strong ill-posedness of logarithmically regularized 2D Euler equations in the borderline Sobolev Space

Hyunju Kwon

Logarithmically regularized 2D Euler equations are active scalar equations with the non-local velocity $u={\nabla }^{\perp }{\Delta }^{-1}{T}_{\gamma }\omega$ for the scalar $\omega$. Two types of the regularizi…