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Rozenn Texier-Picard, Vitaly A. Volpert (2003)
Revista Matemática Complutense
The work is devoted to reaction-diffusion-convection problems in unbounded cylinders. We study the Fredholm property and properness of the corresponding elliptic operators and define the topological degree. Together with analysis of the spectrum of the linearized operators it allows us to study bifurcations of solutions, to prove existence of convective waves, and to make some conclusions about their stability.
Zaher Mahjoub (1983)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Chelkak, S., Koshelev, A., Oganesyan, L. (1997)
Memoirs on Differential Equations and Mathematical Physics
Michael Struwe (1995)
Mathematische Annalen
Zhuan Ye (2015)
Colloquium Mathematicae
We prove the existence and uniqueness of global strong solutions to the Cauchy problem for 3D incompressible MHD equations with nonlinear damping terms. Moreover, the preliminary L² decay for weak solutions is also established.
Daniel Wachsmuth (2005)
Control and Cybernetics
Alexis Vasseur (2009)
Applications of Mathematics
In this short note we give a link between the regularity of the solution to the 3D Navier-Stokes equation and the behavior of the direction of the velocity . It is shown that the control of in a suitable norm is enough to ensure global regularity. The result is reminiscent of the criterion in terms of the direction of the vorticity, introduced first by Constantin and Fefferman. However, in this case the condition is not on the vorticity but on the velocity itself. The proof, based on very...
Nana Pan, Jishan Fan, Yong Zhou (2021)
Applications of Mathematics
We prove a regularity criterion for a nonhomogeneous incompressible Ginzburg-Landau-Navier-Stokes system with the Coulomb gauge in . It is proved that if the velocity field in the Besov space satisfies some integral property, then the solution keeps its smoothness.
Fan, Jishan, Ozawa, Tohru (2008)
Journal of Inequalities and Applications [electronic only]
Gala, Sadek (2010)
Electronic Journal of Differential Equations (EJDE) [electronic only]
He, Cheng (2002)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Luo, Yuwen (2010)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Zdeněk Skalák, Petr Kučera (2003)
Applications of Mathematics
In the context of the weak solutions of the Navier-Stokes equations we study the regularity of the pressure and its derivatives in the space-time neighbourhood of regular points. We present some global and local conditions under which the regularity is further improved.
Skalak, Zdenek (2005)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Luo, Yuwen (2009)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Alami-Idrissi, A., Khabid, S. (2004)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Piotr Kacprzyk (2010)
Applicationes Mathematicae
Existence of a global attractor for the Navier-Stokes equations describing the motion of an incompressible viscous fluid in a cylindrical pipe has been shown already. In this paper we prove the higher regularity of the attractor.
E Acerbi, G Mingione, G. A. Seregin (2004)
Annales de l'I.H.P. Analyse non linéaire
Bochev, P.B., Lehoucq, R.B. (2006)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
Christine Bernardi, Yvon Maday (1990)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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