6 papers · 2 filters
Formalization of the Galerkin Construction for the Two-Dimensional Navier--Stokes Equations in Lean
Weinan Wang
We formalize in Lean 4 the Galerkin construction of global Leray--Hopf weak solutions for the unforced two-dimensional Navier--Stokes equations on arbitrary bounded open domains wi…
Uniform bounds for a thermo-diffusive system beyond exponential growth
Weinan Wang
In this paper, we prove a global-in-time uniform bound for solutions to a thermo-diffusive system in the whole space with bounded nonnegative initial data. The result allows expone…
The entropy production is not always monotone for the Kac equation
Weinan Wang
In 1966, McKean conjectured that the entropy production of Kac's caricature of a Maxwellian gas is nonincreasing in time \cite{McKean66}. We disprove this conjecture for the standa…
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…