Author:
Li Fucai,Zhang Shuxing,Zhang Zhipeng
Abstract
Abstract
In this paper, we study the uniform regularity and zero capillarity-viscosity limit for an inhomogeneous incompressible fluid model of Korteweg type in the half-space
R
+
3
. We consider the Navier-slip boundary condition for velocity and the Dirichlet boundary condition for the gradient of density. By establishing the conormal energy estimates, we prove that there exists a unique strong solution of the model in a finite time interval
[
0
,
T
0
]
, where T
0 is independent of the capillary and viscosity coefficients, and the solution is uniformly bounded in a conormal Sobolev space. Based on the aforementioned uniform estimates, we further show that there exists a constant
0
<
T
1
⩽
T
0
, such that the solutions of this model converge to the solution of the inhomogeneous incompressible Euler equations with the rates of convergence in
L
∞
(
0
,
T
1
;
L
2
(
R
+
3
)
)
and
L
∞
(
0
,
T
1
;
H
1
(
R
+
3
)
)
, as the capillary and viscosity coefficients tend to zero simultaneously.
Funder
a foundation of Laboratory of Computational Physics
the National Natural Science Foundation of China
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics