Pylyp Cherevan

collaborators

4 papers

math.GM2025

An Îµ-free rank-6 decoupling estimate for the paraboloid surface

Pylyp Cherevan

For the paraboloid decomposition $F = \sum_{I^} F_{I^} $ with $I^ \subset ∣ I^¾∣ \sim I^»$ and radius $r = I^»^{- 2/3}$ , we prove a log-free estimate $|F|{L^{6}(QÎ»)}\lesssim Î»^{Î£_Î»} D^{Î£_{D}}…

math.AP2025

Log-free estimate of the full nonlinearity in the three-dimensional Navier-Stokes equations outside the diagonal regime

Pylyp Cherevan

We investigate the contribution of the full nonlinearity outside the narrow diagonal zone in the three-dimensional Navier-Stokes equations. We consider the off-diagonal components,…

math.AP2025

A log-free estimate for the diagonal paraproduct high $\times$ high $\to$ low in the 3D Navier-Stokes equation

Pylyp Cherevan

We consider the diagonal paraproduct arising in the nonlinearity $(u \cdot \nabla) u$ for the three-dimensional Navier-Stokes equations. On scale-critical windows and in the range $…

math.AP2025

Log-free estimate for the resonant paraproduct in the 3D Navier-Stokes equations

Pylyp Cherevan

We consider the resonant paraproduct (high-high $\to$ low regime) in the nonlinearity $(u \cdot \nabla) u$ for the three-dimensional Navier-Stokes equations. For sufficiently smooth,…

An Îµ-free rank-6 decoupling estimate for the paraboloid surface

Log-free estimate of the full nonlinearity in the three-dimensional Navier-Stokes equations outside the diagonal regime

A log-free estimate for the diagonal paraproduct high × high → low in the 3D Navier-Stokes equation

Log-free estimate for the resonant paraproduct in the 3D Navier-Stokes equations

A log-free estimate for the diagonal paraproduct high $\times$ high $\to$ low in the 3D Navier-Stokes equation