Oblak, Blagoje
Published in
Journal of Mathematical Fluid Mechanics

We study the parameter space of cnoidal waves—the periodic solitons of the Korteweg–de Vries equation—from the perspective of Virasoro coadjoint orbits. The monodromy method familiar from inverse scattering implies that many, but not all, of these solitons are conformally equivalent to uniform field configurations (constant coadjoint vectors). The ...

Berselli, Luigi C. Longo, Placido
Published in
Journal of Mathematical Fluid Mechanics

We consider the boundary value problem associated with the divergence operator on a bounded regular subset of Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb...

Kwon, Young-Sam Lin, Ying-Chieh Su, Cheng-Fang
Published in
Journal of Mathematical Fluid Mechanics

In this paper we consider the compressible models of magnetohydrodynamic flows giving rise to a variety of mathematical problems in many areas. We study the asymptotic limit for the compressible rotational magnetohydrodynamic flows with the well-prepared initial data such that we derive a rigorous quasi-geostrophic equation with diffusion term gove...

Wang, Dehua Wu, Jiahong Ye, Zhuan
Published in
Journal of Mathematical Fluid Mechanics

The global well-posedness of the smooth solution to the three-dimensional (3D) incompressible micropolar equations is a difficult open problem. This paper focuses on the 3D incompressible micropolar equations with fractional dissipations (-Δ)αu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{...

Beirão da Veiga, Hugo Yang, Jiaqi
Published in
Journal of Mathematical Fluid Mechanics

In this note we extend a 2018 result of Bardos and Titi (Arch Ration Mech Anal 228(1):197–207, 2018) to a new class of functional spaces Cλ0,α(Ω¯)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}...

Kuang, Jie Zhao, Qin
Published in
Journal of Mathematical Fluid Mechanics

In this paper, we are concerned with the global existence and stability of strong shock front for one-dimensional piston problem. We use the exothermically reacting Euler equations as a mathematical model to describe the gas motion. Under the assumptions that the total variations of initial data and the perturbation of piston velocity are sufficien...

Brzeźniak, Zdzisław Dhariwal, Gaurav
Published in
Journal of Mathematical Fluid Mechanics

Röckner and Zhang (Probab Theory Relat Fields 145, 211–267, 2009) proved the existence of a unique strong solution to a stochastic tamed 3D Navier–Stokes equation in the whole space and for the periodic boundary case using a result from Stroock and Varadhan (Multidimensional diffusion processes, Springer, Berlin, 1979). In the latter case, they als...

Wu, Fan
Published in
Journal of Mathematical Fluid Mechanics

In this paper, we consider the three-dimensional (3D) incompressible double-diffusive convection equations. By making use of a anisotropic Sobolev’s inequality, we obtain a blowup criterion for the strong solution to the 3D double-diffusive convection equations involving only the middle eigenvalue of the strain tensor in anisotropic Lebesgue spaces...

Kagei, Yoshiyuki Teramoto, Yuka
Published in
Journal of Mathematical Fluid Mechanics

The spectrum of the linearized operator around the Couette flow of the compressible Navier–Stokes equations between two concentric rotating cylinders is studied when the Mach number is sufficiently small. It is shown that, for sufficiently small Mach numbers, the linearized operator around the Couette flow has a critical eigenvalue which crosses th...

Panasenko, G. P. Stavre, R.
Published in
Journal of Mathematical Fluid Mechanics

An interaction between a thin cylindrical elastic tube and a viscous fluid filling the thin interior of the elastic tube is considered when the thickness of the elastic medium (ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upg...