5 papers · 1 filter
A note on relativistic kinetic Schauder estimates
Weinan Wang
In this note, motivated by \cite{DW26}, we construct counterexamples to momentum-only Schauder estimates for linear kinetic equations with relativistic transport. The construction…
Exponential decay for the 3D Boussinesq equations with Navier boundary conditions
Wen Feng, Weinan Wang, Xiang Xu
We study the three-dimensional incompressible Boussinesq equations on a bounded domain with smooth boundary and Navier boundary conditions. We construct global weak solutions by a…
Several counterexamples to kinetic Schauder estimates
Hongjie Dong, Weinan Wang
In this paper, we construct counterexamples to the Schauder estimate for kinetic Fokker--Planck equations, disproving \cite[Conjecture~1.3]{HW}. The conjectured estimate would cont…
On a partial data inverse problem for the semi-linear wave equation
Boya Liu, Weinan Wang
We show that a partial Dirichlet-to-Neumann map, where the measurement set is arbitrarily small, uniquely determines the time-dependent nonlinearity of order three or higher in a s…
Asymptotic stability for the 3D Navier-Stokes equations in and nearby spaces
Zachary Bradshaw, Weinan Wang
We provide a short proof of -asymptotic stability around vector fields that are small in weak-, including small Landau solutions. We show that asymptotic stability also h…