10 citations · 51 across the 31 of their papers we have counts for
20 papers · 1 filter
The viscosity limit of fluid flows with growth/decay conditions at infinity
R. McOwen, P. Topalov
We prove that the Navier-Stokes equation is well-posed in function spaces on , , that contain vector fields of order as with …
Spatial decay/asymptotics in the Navier-Stokes equation
Peter Topalov
We discuss the appearance of spatial asymptotic expansions of solutions of the Navier-Stokes equation on . In particular, we prove that the Navier-Stokes equation is…
Spatial asymptotic expansions in the Navier-Stokes equation
R. McOwen, P. Topalov
We prove that the Navier-Stokes equation for a viscous incompressible fluid in is locally well-posed in spaces of functions allowing spatial asymptotic expansions wi…
Spatially quasi-periodic solutions of the Euler equation
Xu Sun, Peter Topalov
We develop a framework for studying quasi-periodic maps and diffeomorphisms on . As an application, we prove that the Euler equation is locally well posed in a space…
Perfect fluid flows on with growth/decay conditions at infinity
Robert McOwen, Peter Topalov
We study the well-posedness and the spatial behavior at infinity of perfect fluid flows on with initial data in a scale of weighted Sobolev spaces that allow spatial growth/…
Sharp well-posedness results of the Benjamin-Ono equation in and qualitative properties of its solution
P. Gérard, T. Kappeler, P. Topalov
We prove that the Benjamin--Ono equation on the torus is globally in time well-posed in the Sobolev space for any and ill-posed for $s \l…