5 papers
Global well-posedness for the incompressible Euler equations in an endpoint Sobolev space
Raphaël Danchin, In-Jee Jeong
We consider the initial value problem for the vorticity equation in the endpoint critical Sobolev space for . In two dimensions, we prove global…
The one-dimensional compressible Navier-Stokes equations in critical regularity spaces
Raphaël Danchin
We are concerned with the barotropic compressible Navier-Stokes equations on the real line. Our primary goal is to establish the global well-posedness in a critical regularity fram…
An elementary approach to the pressureless Euler-Navier-Stokes system
Raphaël Danchin
The pressureless Euler-Navier-Stokes system can be obtained formally from the Vlasov-Navier-Stokes system, under the assumption that the distribution function describing the densit…
Fujita-Kato Solutions and Optimal Time Decay for the Vlasov-Navier-Stokes System in the Whole Space
Raphaël Danchin
We are concerned with the construction of global-in-time strong solutions for the incompressible Vlasov-Navier-Stokes system in the whole three-dimensional space. One of our goals…
Large-time asymptotics of periodic two-dimensional Vlasov-Navier-Stokes flows
Raphaël Danchin, Ling-Yun Shou
We study the large-time behavior of finite-energy weak solutions for the Vlasov-Navier-Stokes equations in a two-dimensional torus. We focus first on the homogeneous case where the…