Global strong solution of the Navier-Stokes equations in 4 and 5 dimensional unbounded domains
Hideo Kozono, Hermann Sohr (1999)
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.
Emmanuel Trélat (2006)
Annales de l'I.H.P. Analyse non linéaire
Michael Ruzhansky, James Smith (2005)
Journées Équations aux dérivées partielles
Global time estimates of norms of solutions to general strictly hyperbolic partial differential equations are considered. The case of special interest in this paper are equations exhibiting the dissipative behaviour. Results are applied to discuss time decay estimates for Fokker-Planck equations and for wave type equations with negative mass.
A. Freiere (1996)
Manuscripta mathematica
Shouquan Ma, Guixiang Xu (2010)
Applicationes Mathematicae
We establish the Strichartz estimates for the linear fractional beam equations in Besov spaces. Using these estimates, we obtain global well-posedness for the subcritical and critical defocusing fractional beam equations. Of course, we need to assume small initial data for the critical case. In addition, by the convexity method, we show that blow up occurs for the focusing fractional beam equations with negative energy.
Houssem Eddine Khochemane, Sara Labidi, Sami Loucif, Abdelhak Djebabla (2025)
Mathematica Bohemica
We consider a one-dimensional porous-elastic system with porous-viscosity and a distributed delay of neutral type. First, we prove the global existence and uniqueness of the solution by using the Faedo-Galerkin approximations along with some energy estimates. Then, based on the energy method with some appropriate assumptions on the kernel of neutral delay term, we construct a suitable Lyapunov functional and we prove that, despite of the destructive nature of delays in general, the damping mechanism...
Changxing Miao, Guixiang Xu, Lifeng Zhao (2009)
Annales de l'I.H.P. Analyse non linéaire
Baoxiang Wang, Lijia Han, Chunyan Huang (2009)
Annales de l'I.H.P. Analyse non linéaire
Tao, Terence (2005)
The New York Journal of Mathematics [electronic only]
Qionglei Chen, Liya Jiang (2014)
Colloquium Mathematicae
We prove the global well-posedness of the 2-D Boussinesq system with temperature dependent thermal diffusivity and zero viscosity coefficient.
Xueshang Feng (1994)
Manuscripta mathematica
O.V. Kapustyan, A.V. Pankov (2014)
Nonautonomous Dynamical Systems
In this paper we prove the existence of a global φ-attractor in the weak topology of the natural phase space for the family of multi-valued processes generated by solutions of a nonautonomous modified 3D Bénard system in unbounded domains for which Poincaré inequality takes place.
Christian Licht, Gérard Michaille (2002)
Annales mathématiques Blaise Pascal
L. A. Peletier, J. Serrin (1978)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Gary M. Lieberman (1994)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Chao Zhang, Shulin Zhou, Bin Ge (2015)
Annales Polonici Mathematici
Under some assumptions on the function p(x), we obtain global gradient estimates for weak solutions of the p(x)-Laplacian type equation in .
Yao, Fengping (2010)
Journal of Inequalities and Applications [electronic only]
M. Bertoldi, S. Fornaro (2004)
Studia Mathematica
We study, with purely analytic tools, existence, uniqueness and gradient estimates of the solutions to the Neumann problems associated with a second order elliptic operator with unbounded coefficients in spaces of continuous functions in an unbounded open set Ω in .
Nguyen Ngoc Khanh (2016)
Archivum Mathematicum
In this paper, we consider gradient estimates on complete noncompact Riemannian manifolds for the following general heat equation where is a constant and is a differentiable function defined on . We suppose that the Bakry-Émery curvature and the -dimensional Bakry-Émery curvature are bounded from below, respectively. Then we obtain the gradient estimate of Li-Yau type for the above general heat equation. Our results generalize the work of Huang-Ma ([4]) and Y. Li ([6]), recently.