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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.
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.
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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