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On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications

Lars Diening, Josef Málek, Mark Steinhauer (2008)

ESAIM: Control, Optimisation and Calculus of Variations

We study properties of Lipschitz truncations of Sobolev functions with constant and variable exponent. As non-trivial applications we use the Lipschitz truncations to provide a simplified proof of an existence result for incompressible power-law like fluids presented in [Frehse et al., SIAM J. Math. Anal34 (2003) 1064–1083]. We also establish new existence results to a class of incompressible electro-rheological fluids.

On the Cauchy problem for the equations of ideal compressible MHD fluids with radiation

Christian Rohde, Wojciech M. Zajączkowski (2003)

Applications of Mathematics

We consider a system of balance laws describing the motion of an ionized compressible fluid interacting with magnetic fields and radiation effects. The local-in-time existence of a unique smooth solution for the Cauchy problem is proven. The proof follows from the method of successive approximations.

On the magnetohydrodynamic type equations in a new class of non-cylindrical domains

Luigi C. Berselli, Jorge Ferreira (1999)

Bollettino dell'Unione Matematica Italiana

Viene provata l'esistenza e l'unicità delle soluzioni deboli per un sistema di equazioni della magnetoidrodinamica in un dominio variabile. Per la dimostrazione si usano il metodo di Galerkin spettrale e la tecnica introdotta da Dal Passo e Ughi per trattare i problemi con dominio dipendente dal tempo.

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