3 citations · 11 across the 21 of their papers we have counts for
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On self-similar solutions to degenerate compressible Navier-Stokes equations
Pierre Germain, Tsukasa Iwabuchi, Tristan Léger
We study cavitating self-similar solutions to compressible Navier-Stokes equations with degenerate density-dependent viscosity. We prove both existence of expanders and non-existen…
Backward self-similar solutions for compressible Navier-Stokes equations
Pierre Germain, Tsukasa Iwabuchi, Tristan Léger
This article is devoted to backward self-similar blow up solutions of the compressible Navier-Stokes equations with radial symmetry. We show that such solutions cannot exist if the…
The Leibniz rule for the Dirichlet and the Neumann Laplacian
Tsukasa Iwabuchi
We study the bilinear estimates in the Sobolev spaces with the Dirichlet and the Neumann boundary condition. The optimal regularity is revealed to get such estimates in the half sp…
Self-similar solutions for compressible Navier-Stokes equations
Pierre Germain, Tsukasa Iwabuchi
We construct forward self-similar solutions (expanders) for the compressible Navier-Stokes equations. Some of these self-similar solutions are smooth, while others exhibit a singul…