Mitra, Sourav
Published in
Journal of Mathematical Fluid Mechanics

We are interested in studying a system coupling the compressible Navier–Stokes equations with an elastic structure located at the boundary of the fluid domain. Initially the fluid domain is rectangular and the beam is located on the upper side of the rectangle. The elastic structure is modeled by an Euler–Bernoulli damped beam equation. We prove th...

Huang, Bingkang
Published in
Journal of Mathematical Fluid Mechanics

Compressible micropolar equations model a class of fluids with microstructure. In this paper we establish the dissipative measure-valued solution to the micropolar fluids. We also give the weak-strong uniqueness principle to this system which means its dissipative measure-valued solution is the same as the classical solution, provided they emanate ...

Essaouini, Hilal Capodanno, Pierre
Published in
Journal of Mathematical Fluid Mechanics

We study the small oscillations of a system of two nonmixing fluids, the upper inviscid, the lower viscoelastic, in an open container, restricting ourselves for the second to the more simple Oldroyd model. At first, we write the equations of motion of the system. Introducing the displacements potential of the inviscid fluid, that depends on the def...

Debbi, Latifa
Published in
Journal of Mathematical Fluid Mechanics

We introduce and study the well posedness: global existence, uniqueness and regularity of the solutions, of a class of d-dimensional fractional stochastic active scalar equations defined either on the torus Td\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepa...

Tice, Ian Zbarsky, Samuel
Published in
Journal of Mathematical Fluid Mechanics

In this paper we consider a slab of viscous incompressible fluid bounded above by a free boundary, bounded below by a flat rigid interface, and acted on by gravity. The unique equilibrium is a flat slab of quiescent fluid. It is well-known that equilibria are asymptotically stable but that the rate of decay to equilibrium depends heavily on whether...

Degond, Pierre Merino-Aceituno, Sara Vergnet, Fabien Yu, Hui
Published in
Journal of Mathematical Fluid Mechanics

This note provides a list of errata and their correction for Reference [1].

Yang, Shaojie
Published in
Journal of Mathematical Fluid Mechanics

In this paper, we prove generic regularity of energy conservative solutions to the rotation Camassa–Holm equation, which can be considered as a model in the shallow water for the long-crested waves propagating near the equator with effect of the Coriolis force due to the Earth’s rotation.

Korobkov, Mikhail V. Pileckas, Konstantin Russo, Remigio
Published in
Journal of Mathematical Fluid Mechanics

It is proved that a distributional solution u to the stationary Navier–Stokes equations in a bounded domain Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega $$\e...

Wang, Xiang Wang, Ya-Guang
Published in
Journal of Mathematical Fluid Mechanics

The proposal of this paper is to study the local existence of analytic solutions, and blowup of solutions in a finite time for the geophysical boundary layer problem. In contrast with the classical Prandtl boundary layer equation, the geophysical boundary layer equation has an additional integral term arising from the Coriolis force. Under the assu...

Wei, Long
Published in
Journal of Mathematical Fluid Mechanics

In this paper, the blow-up phenomenon, global existence and persistent decay of the solutions to the Gurevich–Zybin system are studied. We show that the system possesses a so called critical threshold phenomena, that is, global smoothness versus finite time breakdown depends on whether the initial configuration crosses an intrinsic critical thresho...