Keiichi Watanabe

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20022021

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6 papers · 1 filter

math.AP2020

Local well-posedness of incompressible viscous fluids in bounded cylinders with $9 0^{\circ}$ -contact angle

Keiichi Watanabe

We consider a free boundary problem of the Navier--Stokes equations in the three-dimensional Euclidean space with moving contact line, where the 90 $^{\circ}$ -contact angle condition…

math.AP2019

Global existence of the Navier-Stokes-Korteweg equations with a non-decreasing pressure in $L^{p}$ -framework

Keiichi Watanabe

We consider the isentropic Navier-Stokes-Korteweg equations with a non-decreasing pressure on the whole space $R^{n}$ $(n \geq 2)$ , where the system describes the motion of c…

math.AP2019

The Navier--Stokes equations in exterior Lipschitz domains: $L^{p}$ -theory

Patrick Tolksdorf, Keiichi Watanabe

We show that the Stokes operator defined on $L_{σ}^{p} (Ω)$ for an exterior Lipschitz domain $Ω \subset R^{n}$ $(n \geq 3)$ admits maximal regularity provided that $p$ s…

math.AP2018

Global solvability of compressible-incompressible two-phase flows with phase transitions in bounded domains

Keiichi Watanabe

Consider a free boundary problem of compressible-incompressible two-phase flows with surface tension and phase transition in bounded domains $Ω_{t +}, Ω_{t -} \subset R^{N}$ …

math.AP2018

Strong solutions to compressible-incompressible two-phase flows with phase transitions

Keiichi Watanabe

We consider a free boundary problem of compressible-incompressible two-phase flows with phase transitions in general domains of $N$ -dimensional Euclidean space (e.g. whole space; h…

math.AP2017

Compressible-incompressible two-phase flows with phase transition: model problem

Keiichi Watanabe

We study the compressible and incompressible two-phase flows separated by a sharp interface with a phase transition and a surface tension. In particular, we consider the problem in…

Local well-posedness of incompressible viscous fluids in bounded cylinders with 90∘-contact angle

Global existence of the Navier-Stokes-Korteweg equations with a non-decreasing pressure in Lp-framework

The Navier--Stokes equations in exterior Lipschitz domains: Lp-theory

Global solvability of compressible-incompressible two-phase flows with phase transitions in bounded domains

Strong solutions to compressible-incompressible two-phase flows with phase transitions

Compressible-incompressible two-phase flows with phase transition: model problem

Local well-posedness of incompressible viscous fluids in bounded cylinders with $9 0^{\circ}$ -contact angle

Global existence of the Navier-Stokes-Korteweg equations with a non-decreasing pressure in $L^{p}$ -framework

The Navier--Stokes equations in exterior Lipschitz domains: $L^{p}$ -theory