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We study a spherical, self-gravitating fluid model, which finds applications in cosmic structure formation. We argue that since the system features nonlinearity and gravity-induced dispersion, the emergence of solitons becomes possible. We…

Pattern Formation and Solitons · Physics 2024-02-21 G. N. Koutsokostas , S. Sypsas , O. Evnin , T. P. Horikis , D. J. Frantzeskakis

This paper is devoted to studying the inflow problem for an ideal polytropic model with non-viscous gas in one-dimensional half space. We showed the existence of the boundary layer in different areas. By employing the energy method, we also…

Analysis of PDEs · Mathematics 2018-06-01 Meichen Hou , Lili Fan

This paper concerns the dynamics of a layer of incompressible viscous fluid lying above a vertically oscillating rigid plane and with an upper boundary given by a free surface. We consider the problem with gravity and surface tension for…

Analysis of PDEs · Mathematics 2019-05-14 David Altizio , Ian Tice , Xinyu Wu , Taisuke Yasuda

The hard phase model describes a relativistic barotropic fluid with sound speed equal to the speed of light. In the framework of general relativity, the motion of the fluid is coupled to the Einstein equations which describe the structure…

Analysis of PDEs · Mathematics 2024-05-27 Zeming Hao , Shuang Miao

The instability of flows via two-dimensional perturbations is analyzed theoretically and numerically in a nonmodal framework. The analysis is based on results obtained in [Verschaeve et al. (2018)] showing the inviscid character of the…

Fluid Dynamics · Physics 2020-02-25 Joris C. G. Verschaeve

A comprehensive, temporal and spatiotemporal linear stability analyses of a (driven) Oldroyd-B fluid with Poiseuille base flow profile in a horizontally aligned, square, Hele-Shaw cell is reported to identify the viable regions of…

Fluid Dynamics · Physics 2022-10-26 D. Bansal , T. Chauhan , S. Sircar

In this paper, we consider an incompressible viscous fluid in an infinitely deep ocean, being bounded above by a free moving boundary. The governing equations are the gravity-driven incompressible Navier-Stokes equations with variable…

Analysis of PDEs · Mathematics 2025-02-12 Tien-Tai Nguyen

We study a fluid-structure interaction problem between a viscous incompressible fluid and an elastic beam with fixed endpoints in a static setting. The 3D fluid domain is bounded, nonsmooth and non simply connected, the fluid is modeled by…

Analysis of PDEs · Mathematics 2026-01-30 Vincenzo Bianca , Edoardo Bocchi , Filippo Gazzola

For a general class of hyperbolic-parabolic systems including the compressible Navier-Stokes and compressible MHD equations, we prove existence and stability of noncharacteristic viscous boundary layers for a variety of boundary conditions…

Analysis of PDEs · Mathematics 2015-05-13 Olivier Gues , Guy Metivier , Mark Williams , Kevin Zumbrun

Motion in the atmosphere or mantle convection are two among phenomena of natural convection induced by internal heat sources. They bifurcate from the conduction state as a result of its loss of stability. In spite of their importance, due…

Mathematical Physics · Physics 2007-05-23 Ioana Dragomirescu , Adelina Georgescu

We consider the hydrodynamics of an incompressible fluid on a 2D periodic domain. There exists a family of stationary solutions with vorticity given by $\Omega^*=\alpha\cos (\mathbf{p} \cdot \mathbf{x} )+\beta \sin (\mathbf{p} \cdot…

Dynamical Systems · Mathematics 2016-08-26 Joachim Worthington , Holger R. Dullin , Robert Marangell

The manuscript focuses on the theoretical stability analysis of the viscous liquid over a vibrating inclined rigid bed when the fluid undergoes an impact of odd viscosity. Such an impact emerges in the classical fluid owing to the broken…

Fluid Dynamics · Physics 2024-10-01 Md. Mouzakkir Hossain , Mrityunjoy Saha , Harekrushna Behera , Sukhendu Ghosh

A diffused interface model describing the evolution of two conterminous incompressible fluids in a porous medium is discussed. The system consists of the Cahn-Hilliard equation with Flory-Huggins logarithmic potential, coupled via surface…

Analysis of PDEs · Mathematics 2024-07-24 Nitu Lakhmara , Hari Shankar Mahato

Structured on the paradigmatic Navier-Stokes flow model, we study a stochastically forced Taylor-Couette system in the narrow gap limit, in order to analyze the simultaneous impact of a non-conserved (Gaussian) force and a nonlinear…

Fluid Dynamics · Physics 2020-04-22 Larry E. Godwin , Sotos C. Generalis , Amit K. Chattopadhyay

We study the linear stability of elastic collapsible tubes conveying fluid, when the equilibrium configuration of the tube is helical. A particular case of such tubes, commonly encountered in applications, is represented by quarter- or…

Chaotic Dynamics · Physics 2018-03-14 François Gay-Balmaz , Dimitri Georgievskii , Vakhtang Putkaradze

We consider the linear stability of Hill's vortex with respect to axisymmetric perturbations. Given that Hill's vortex is a solution of a free-boundary problem, this stability analysis is performed by applying methods of shape…

Fluid Dynamics · Physics 2016-08-24 Bartosz Protas , Alan Elcrat

It is well known that the linear stability of solutions of partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the…

Exactly Solvable and Integrable Systems · Physics 2018-06-18 Antonio Degasperis , Sara Lombardo , Matteo Sommacal

We consider the Stokes eigenvalue problem in a bounded domain of R3 with Dirich- let boundary conditions. The aim of this paper is to advance the development of high-order terms in the asymptotic expansions of the boundary perturbations of…

Mathematical Physics · Physics 2016-12-22 Christian Daveau , Abdessatar Khelifi

A nonlocal interface equation is derived for two-phase fluid flow, with arbitrary wettability and viscosity contrast c=(mu_1-mu_2)/(mu_1+mu_2), in a model porous medium defined as a Hele-Shaw cell with random gap b_0+delta b. Fluctuations…

Statistical Mechanics · Physics 2009-11-07 E. Paune , J. Casademunt

We prove eigenvalue bounds for two-dimensional linearized disturbances of parallel flows of micropolar fluids, deriving the Orr-Sommerfeld equations and providing a sufficient condition for linear stability of such flows. We also derive…

Analysis of PDEs · Mathematics 2024-09-19 Pablo Braz e Silva , Jackellyny Carvalho