arXiv subjects
Publications and source records attributed to Karen Zaya.
We prove that a solution to the three-dimensional Boussinesq equations does not blow-up at time T if $\| u_{\le Q}\|_{B^1_{\infty, \infty}}$ is integrable on $(0, T)$, where $u_{\le Q }$ represents the low modes of Littlewood-Paley projection of the velocity $u$.
We improve previous known lower bounds for Sobolev norms of potential blow-up solutions to the three-dimensional Navier-Stokes equations in $\dot{H}^\frac{3}{2}$. We also present an alternate proof for the lower bound for the $\dot{H}^\frac{5}{2}$ blow-up.
We study the inviscid dyadic model of the Euler equations and prove some regularizing properties of the nonlinear term that occur due to forward energy cascade. We show every solution must have 3/5 L^2-based (or 1/10 L^3-based) regularity for all positive time. We conjecture this holds up to Onsager's scaling, where the L^2-based exponent is 5/6 and the L^3-based exponent is 1/3.