On instability of a generic compressible two-fluid model in R3
نویسندگان
چکیده
We are concerned with the instability of a generic compressible two-fluid model in whole space $\mathbb{R}^3$, where capillary pressure $f(\alpha^-\rho^-)=P^+-P^-\neq 0$ is taken into account. For case that strictly decreasing function near equilibrium, namely, $f'(1)<0$, Evje-Wang-Wen established global stability constant equilibrium state for three-dimensional Cauchy problem under some smallness assumptions. Recently, Wu-Yao-Zhang proved $P^+=P^-$ (corresponding to $f'(1)=0$). In this work, we investigate increasing $f'(1)>0$. First, by employing Hodge decomposition technique and making detailed analysis Green's corresponding linearized system, construct solutions grow exponentially time Sobolev $H^k$, thus leading result problem. Moreover, help linear local existence theorem classical original nonlinear can then show sense Hadamard delicate on properties semigroup. Therefore, our shows $f'(1)>0$, linearly globally unstable nonlinearly locally Hadamard, which contrast cases $f'(1)<0$ $f'(1)=0$) two--fluid stable.
منابع مشابه
Rayleigh-Taylor Instability in a Compressible Fluid
Rayleigh-Taylor instability in a compressible fluid is reconsidered. The density is allowed to vary with pressure under the barotropy assumption. For the case with equal speeds of sound in the two superposed fluids, in order to give a non-trivial compressibility correction to the Rayleigh-Taylor growth rate, the compressibility correction is calculated to O(g/ka). To this order, compressibility...
متن کاملTwo-fluid compressible simulations on GPU cluster
In this work we propose an efficient finite volume approximation of twofluid flows. Our scheme is based on three ingredients. We first construct a conservative scheme that removes the pressure oscillations phenomenon at the interface. The construction relies on a random sampling at the interface [6, 5]. Secondly, we replace the exact Riemann solver by a faster relaxation Riemann solver with goo...
متن کاملSelf Gravitating Instability of a Compressible Fluid Cylinder
The self-gravitating instability of a compressible-inviscid fluid cylinder immersed into a self-gravitating tenuous medium of negligible motion is developed. The stability criterion is derived based on the linear perturbation technique. Some previous reported works are recovered. The effect of different factors on the fluid cylinder instability is discussed. The compressibility has a tendency f...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Nonlinearity
سال: 2023
ISSN: ['0951-7715', '1361-6544']
DOI: https://doi.org/10.1088/1361-6544/ace818