%Aigaion2 BibTeX export from Bibliography database
%Wednesday 13 May 2026 08:51:46 PM

@ARTICLE{,
            author = {Bathory, Michal and Bul{\'{\i}}{\v c}ek, Miroslav and M{\'{a}}lek, Josef},
             title = {Large data existence theory for three-dimensional unsteady flows of rate-type viscoelastic fluids with stress diffusion},
           journal = {Advances in Nonlinear Analysis},
            volume = {10},
            number = {1},
              year = {2021},
             pages = {501--521},
               doi = {10.1515/anona-2020-0144},
          abstract = {We prove that there exists a weak solution to a system governing an unsteady flow of a viscoelastic fluid in three dimensions, for arbitrarily large time interval and data. The fluid is described by the incompressible Navier-Stokes equations for the velocity $\ve$, coupled with a diffusive variant of a combination of the Oldroyd-B and the Giesekus models for a tensor $\B$. By a proper choice of the constitutive relations for the Helmholtz free energy %Cauchy stress tensor $\T$
	(which, however, is non-standard in the current literature  despite the fact that this choice is well motivated from the point of view o physics) and for the energy dissipation, we are able to prove that $\B$ enjoys the same regularity as $\ve$ in the classical three-dimensional Navier-Stokes equations. This enables us to handle any kind of objective derivative of $\B$, thus obtaining existence results for the class of diffusive Johnson-Segalman models as well. Moreover, using a suitable approximation scheme, we are able to show that $\B$ remains positive definite if the initial datum was a positive definite matrix (in a pointwise sense). We also show how the model we are considering can be derived from basic balance equations and thermodynamical principles in a natural way.},
  Preprint project = {NCMM},
     Preprint year = {2020},
   Preprint number = {01},
       Preprint ID = {NCMM/2020/01}
}