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Marius Paicu (2005)
Revista Matemática Iberoamericana
We study the tridimensional Navier-Stokes equation when the value of the vertical viscosity is zero, in a critical space (invariant by the scaling). We shall prove local in time existence of the solution, respectively global in time when the initial data is small compared with the horizontal viscosity.
H. Abidi (2007)
Revista Matemática Iberoamericana
Jiří Neustupa, Patrick Penel (2005)
Banach Center Publications
We formulate sufficient conditions for regularity up to the boundary of a weak solution v in a subdomain Ω × (t₁,t₂) of the time-space cylinder Ω × (0,T) by means of requirements on one of the eigenvalues of the rate of deformation tensor. We assume that Ω is a cube.
P. Constantin (2008)
Publicacions Matemàtiques
Boldrini, José Luiz, Dias Vaz, Cristina Lúcia (2003)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Rodolfo Salvi (2005)
Banach Center Publications
In the paper [13], we give the full system of equations modelling the motion of a fluid/viscoelastic solid system, and obtain a differential model similar to the so-called Oldroyd model for a viscoelastic fluid. Moreover, existence results in bounded domains are obtained. In this paper we extend the results in [13] to unbounded domains. The unique solvability of the system of equations is established locally in time and globally in time with so-called smallness restrictions. Moreover, existence...
Céline Grandmont, Yvon Maday (2000)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Céline Grandmont, Yvon Maday (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
We study the well-posedness of an unsteady fluid-structure interaction problem. We consider a viscous incompressible flow, which is modelled by the Navier-Stokes equations. The structure is a collection of rigid moving bodies. The fluid domain depends on time and is defined by the position of the structure, itself resulting from a stress distribution coming from the fluid. The problem is then nonlinear and the equations we deal with are coupled. We prove its local solvability in time through two...
Hammadi Abidi, Marius Paicu (2007)
Annales de l’institut Fourier
Dans cet article on s’intéresse à l’existence et l’unicité globale de solutions pour le système de Navier-Stokes à densité variable, lorsque la donnée initiale de la vitesse est dans l’espace de Besov homogène de régularité critique . Notons que ce résultat fait suite aux résultats de H. Abidi qui a généralisé le travail de R. Danchin. Toutefois, dans les travaux antérieurs, l’existence de la solution est obtenue pour et l’unicité est démontrée sous l’hypothèse plus restrictive Notre résultat...
Ramzi, May, Zahrouni, Ezzeddine (2011)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Youcef Amirat, Didier Bresch, Jérôme Lemoine, Jacques Simon (1999)
Rendiconti del Seminario Matematico della Università di Padova
W. M. Zajączkowski (2002)
Hu, Xianpeng (2005)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Kaya, Meryem (2003)
Journal of Applied Mathematics
Cholmin Sin, Sin-Il Ri (2022)
Mathematica Bohemica
We prove the existence of weak solutions for steady flows of electrorheological fluids with homogeneous Navier-slip type boundary conditions provided . To prove this, we show Poincaré- and Korn-type inequalities, and then construct Lipschitz truncation functions preserving the zero normal component in variable exponent Sobolev spaces.
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