D. Gérard-Varet

activity

20062025

most citedOn the ill-posedness of the Prandtl equation

312 citations · 789 across the 22 of their papers we have counts for

collaborators

Showing 2018 · math.APShow all

3 papers · 2 filters

math.AP2018★ 5 cited

Well-posedness of the Prandtl equation without any structural assumption

Helge Dietert, David Gerard-Varet

We show the local in time well-posedness of the Prandtl equation for data with Gevrey $2$ regularity in $x$ and $H^{1}$ regularity in $y$ . The main novelty of our result is that we d…

math.AP2018★ 51 cited

Sobolev stability of Prandtl expansions for the steady Navier-Stokes equations

David Gerard-Varet, Yasunori Maekawa

We show the $H^{1}$ stability of shear flows of Prandtl type: $U^{ν} = (U_{s} (y / ν), 0)$ , in the steady two-dimensional Navier-Stokes equations, under the natural assumptions that $U_s…

math.AP2018

Well-posedness of the hydrostatic Navier-Stokes equations

David Gerard-Varet, Nader Masmoudi, Vlad Vicol

We address the local well-posedness of the hydrostatic Navier-Stokes equations. These equations, sometimes called reduced Navier-Stokes/Prandtl, appear as a formal limit of the Nav…