Maximal $$L^1$$-regularity of the heat equation and application to a free boundary problem of the Navier-Stokes equations near the half-space

2021 ◽  
Author(s):  
Takayoshi Ogawa ◽  
Senjo Shimizu
Keyword(s):  
Free Boundary ◽  
Heat Equation ◽  
Boundary Problem ◽  
Half Space ◽  
Free Boundary Problem ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
A Free Boundary Problem

scholarly journals Classical Solvability of a Free Boundary Problem for an Incompressible Viscous Fluid with a Surface Density Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Yoshiaki Kusaka
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Surface Mass ◽  
A Free Boundary Problem ◽  
Physical Phenomena ◽  
Density Equation

We investigate a mathematical model introduced by Shikhmurzaev to remove singularities that arise when classical hydrodynamic models are applied to certain physical phenomena. The model is described as a free boundary problem consisting of the Navier-Stokes equations and a surface mass balance equation. We prove the local-in-time solvability in Hölder spaces.

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