Šárka Matušů-Nečasová (1992)
Applications of Mathematics
The paper contains the proof of global existence of weak solutions of the viscous compressible barotropic gas for the initial-boundary value problem in a finite channel.
Nesrine Fterich (2010)
Applications of Mathematics
The article deals with a nonlinear generalized Ginzburg-Landau (Allen-Cahn) system of PDEs accounting for nonisothermal phase transition phenomena which was recently derived by A. Miranville and G. Schimperna: Nonisothermal phase separation based on a microforce balance, Discrete Contin. Dyn. Syst., Ser. B, 5 (2005), 753–768. The existence of solutions to a related Neumann-Robin problem is established in an -dimensional space setting. A fixed point procedure guarantees the existence of solutions...
Jindřich Nečas, Antonín Novotný, Miroslav Šilhavý (1989)
Commentationes Mathematicae Universitatis Carolinae
Šárka Matušů-Nečasová (1991)
Applications of Mathematics
The paper contains the proof of global existence of weak solutions viscous compressible isothermal bipolar fluid of initial boundary value in a finite channel.
Lukina, E. V. (2003)
Sibirskij Matematicheskij Zhurnal
Matania Ben-Artzi (1992)
Journées équations aux dérivées partielles
Song Jiang (1998)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
E. Horst (1990)
Piotr Bogusław Mucha (2008)
Banach Center Publications
In this note we present a proof of existence of global in time regular (unique) solutions to the Navier-Stokes equations in an arbitrary three dimensional domain with a general boundary condition. The only restriction is that the L₂-norm of the initial datum is required to be sufficiently small. The magnitude of the rest of the norm is not restricted. Our considerations show the essential role played by the energy bound in proving global in time results for the Navier-Stokes equations.
Nader Masmoudi, Ping Zhang (2005)
Annales de l'I.H.P. Analyse non linéaire
Pecher, Hartmut (2005)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Wojciech M. Zajączkowski (2005)
Hideo Kozono, Takayoshi Ogawa (1994)
Mathematische Zeitschrift
Hideo Kozono, Hermann Sohr (1999)
Annales de l'I.H.P. Analyse non linéaire
F. Planchon (1996)
Annales de l'I.H.P. Analyse non linéaire
Ruikuan Liu, Jiayan Yang (2020)
Applications of Mathematics
The main objective of this paper is to study the global strong solution of the parabolic-hyperbolic incompressible magnetohydrodynamic model in the two dimensional space. Based on Agmon, Douglis, and Nirenberg’s estimates for the stationary Stokes equation and Solonnikov’s theorem on --estimates for the evolution Stokes equation, it is shown that this coupled magnetohydrodynamic equations possesses a global strong solution. In addition, the uniqueness of the global strong solution is obtained.
E. Horst (1987)
Banach Center Publications
R. Farwig, H. Kozono, H. Sohr (2011)
Rendiconti del Seminario Matematico della Università di Padova
Jiří Neustupa (1988)
Aplikace matematiky
The paper contains the proof of global existence of weak solutions to the mixed initial-boundary value problem for a certain modification of a system of equations of motion of viscous compressible fluid. The modification is based on an application of an operator of regularization to some terms appearing in the system of equations and it does not contradict the laws of fluid mechanics. It is assumed that pressure is a known function of density. The method of discretization in time is used and finally,...
Jiří Neustupa, Antonín Novotný (1991)
Applications of Mathematics
The concept of regularization to the complete system of Navier-Stokes equations for viscous compressible heat conductive fluid is developed. The existence of weak solutions for the initial boundary value problem for the modified equations is proved. Some energy and etropy estimates independent of the parameter of regularization are derived.