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math.AP2026
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…
math.AP2026
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…
math.AP2026
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…