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Global strong solutions of a 2-D new magnetohydrodynamic system

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 $L^{p}$ - $L^{q}$ -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.

Global strong solutions of Vlasov's equation---necessary and sufficient conditions for their existence

E. Horst (1987)

Banach Center Publications

Global subanalytic solutions of Hamilton–Jacobi type equations

Emmanuel Trélat (2006)

Annales de l'I.H.P. Analyse non linéaire

Global superconvergence of finite element methods for parabolic inverse problems

Hossein Azari, Shu Hua Zhang (2009)

Applications of Mathematics

In this article we transform a large class of parabolic inverse problems into a nonclassical parabolic equation whose coefficients consist of trace type functionals of the solution and its derivatives subject to some initial and boundary conditions. For this nonclassical problem, we study finite element methods and present an immediate analysis for global superconvergence for these problems, on basis of which we obtain a posteriori error estimators.

Global time estimates for solutions to equations of dissipative type

Michael Ruzhansky, James Smith (2005)

Journées Équations aux dérivées partielles

Global time estimates of $L^{p} - L^{q}$ 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.

Global uniqueness for an inverse boundary problem arising in elasticity.

Gen Nakamura, Gunther Uhlmann (1994)

Inventiones mathematicae

Global uniqueness results for fractional order partial hyperbolic functional differential equations.

Abbas, Saïd, Benchohra, Mouffak, Nieto, Juan J. (2011)

Advances in Difference Equations [electronic only]

Global uniqueness results for fractional partial hyperbolic differential equations with state-dependent delay

Mouffak Benchohra, Mohamed Hellal (2014)

Annales Polonici Mathematici

We investigate the existence and uniqueness of solutions of hyperbolic fractional order differential equations with state-dependent delay by using a nonlinear alternative of Leray-Schauder type due to Frigon and Granas for contraction maps on Fréchet spaces.

Global weak solutions for $1 + 2$ dimensional wave maps into homogeneous spaces

Yi Zhou (1999)

Annales de l'I.H.P. Analyse non linéaire

Global weak solutions for a degenerate parabolic system modelling a one-dimensional compressible miscible flow in porous media

Y. Amirat, A. Ziani (2004)

Bollettino dell'Unione Matematica Italiana

We show the solvability of a nonlinear degenerate parabolic system of two equations describing the displacement of one compressible fluid by another, completely miscible with the first, in a one-dimensional porous medium, neglecting the molecular diffusion. We use the technique of renormalised solutions for parabolic equations in the derivation of a priori estimates for viscosity type solutions. We pass to the limit, as the molecular diffusion coefficient tends to 0, on the parabolic system, owing...

Global weak solutions of the Navier-Stokes equations with nonhomogeneous boundary data and divergence

R. Farwig, H. Kozono, H. Sohr (2011)

Rendiconti del Seminario Matematico della Università di Padova

Global weak solutions of the wave map system to compact homogeneous spaces.

A. Freiere (1996)

Manuscripta mathematica

Global weak solvability of a regularized system of the Navier-Stokes equations for compressible fluid

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,...

Global weak solvability to the regularized viscous compressible heat conductive flow

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.

Global well-posedness and blow up for the nonlinear fractional beam equations

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.