11 papers
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…
Operator learning for the 2D incompressible Navier-Stokes equations: a conformal prediction approach in the data-scarce regime
Weinan Wang, Bowen Gang, Hao Deng
In this paper, we propose a perturbation-based conformal prediction framework for uncertainty quantification in operator learning, with a focus on the 2D Navier--Stokes equations.…
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…
A kinetic Nash inequality and precise boundary behavior of the kinetic Fokker-Planck equation
Christopher Henderson, Giacomo Lucertini, Weinan Wang
In this paper, we prove a kinetic Nash type inequality and adapt it to a new functional inequality for functions in a kinetic Sobolev space with absorbing boundary conditions on th…
Global well-posedness and enhanced dissipation for the 2D stochastic Nernst-Planck-Navier-Stokes equations with transport noise
Quyuan Lin, Rongchang Liu, Weinan Wang
In this paper, we consider the 2D stochastic Nernst-Planck-Navier-Stokes equations with transport noise. By assuming the ionic species have the same diffusivity and opposite valenc…