Neustupa, Jiří Yang, Minsuk
Published in
Journal of Mathematical Fluid Mechanics

We assume that Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega $$\end{document} is either a smooth bounded domain in R3\documentclass[12pt]{minimal} \usepackage...

Wei, Ruiying Li, Yin Yao, Zheng-an
Published in
Journal of Mathematical Fluid Mechanics

In this paper, we are concerned with the global well-posedness and decay rates of strong solutions for the three-dimensional compressible Phan-Thein–Tanner model. We prove that this set of equations admits a unique global strong solution provided the initial data are close to the constant equilibrium state in H3\documentclass[12pt]{minimal} \usepac...

Canon, Éric Chardard, Frédéric Panasenko, Grigory Štikonienė, Olga

A non-stationary flow in a network of thin tubes is considered. Its one-dimensional approximation was proposed in a paper by G.Panasenko and K.Pileckas, Flows in a tube structure: equation on the graph, JMP (2014). It consists of a set of equations with weakly singular kernels, on a graph, for the macroscopic pressure. A new difference scheme for t...

Barker, Tobias Prange, Christophe
Published in
Journal of Mathematical Fluid Mechanics

In this short paper we prove the global regularity of solutions to the Navier–Stokes equations under the assumption that slightly supercritical quantities are bounded. As a consequence, we prove that if a solution u to the Navier–Stokes equations blows-up, then certain slightly supercritical Orlicz norms must become unbounded. This partially answer...

Gala, Sadek Ragusa, Maria Alessandra
Published in
Partial Differential Equations and Applications

In this paper, we study regularity of weak solutions to the incompressible Navier–Stokes equations in R3×(0,T)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R...

Abbatiello, Anna
Published in
Journal of Mathematical Fluid Mechanics

In this study we are interested in the Navier–Stokes-like system for generalized viscous fluids whose viscosity has a power-structure with exponent q. We develop an existence theory of time-periodic three-dimensional flows.

Mohan, Manil T.
Published in
Journal of Mathematical Fluid Mechanics

This work addresses some asymptotic behavior of solutions to stochastic convective Brinkman–Forchheimer (SCBF) equations perturbed by multiplicative Gaussian noise in two and three dimensional bounded domains. Using a weak convergence approach of Budhiraja and Dupuis, we establish the Laplace principle for the strong solution to SCBF equations in a...

Lepe, Felipe Otárola, Enrique Quero, Daniel
Published in
Journal of Scientific Computing

We analyze, on two dimensional polygonal domains, classical low–order inf-sup stable finite element approximations of the stationary Navier–Stokes equations with singular sources. We operate under the assumptions that the continuous and discrete solutions are sufficiently small. We perform an a priori error analysis on convex domains. On Lipschitz,...

Li, Weilong Wang, Wenjun Wang, Yinghui Yao, Lei
Published in
Journal of Mathematical Fluid Mechanics

In this paper, we consider the compressible Navier–Stokes equations without heat conductivity in R3.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}^{3}.$$...

Kirane, Mokhtar Aimene, Djihad Seba, Djamila
Published in
Zeitschrift für angewandte Mathematik und Physik

This paper is a development of the results and techniques of the two papers (Carvalho-Neto and Planas in J Differ Equ 259:2948–2980, 2015; Oka in J Math Anal Appl 473:382–407, 2019) for the aim of addressing the existence and uniqueness of local and global mild solutions, on the Heisenberg group Hd\documentclass[12pt]{minimal} \usepackage{amsmath} ...