Regularity results for parabolic systems related to a class of non-Newtonian fluids

By E. Acerbi, Giuseppe Mingione, G A Seregin. 2004

192 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/f43d74c34b62829b589a697d7e1c8386254c3af5

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Calderón–Zygmund estimates for parabolic p(x,t)-Laplacian systems (2014, background): “As already mentioned before, for more general parabolic systems with non-standard growth partial regularity results can be found in [5, 21].”
Overview of differential equations with non-standard growth (2010, background): “In their introduction to [31], Acerbi, Minginoe and Seregin note that their studies relate to the modeling of electro-rheological fluids.”
Higher integrability for parabolic systems with non-standard growth and degenerate diffusions (2011, unknown): “vector-fields being differentiable with respect to x —or at least Lipschitz continuous with respect to x— higher integrability results can be found in [5], [19], [39].”
Anisotropic parabolic equations with variable nonlinearity (2009, background): “Some properties of solutions of the system of modified nonstationary Navier-Stokes equations describing electro-rheological fluids are studied in [4].”
Harmonic type approximation lemmas (2009, background): “Especially, the functional Dp(x) appears in the modeling of physical situations exhibiting strong inhomogeneities, in particular in the context of non-newtonian fluid-dynamics (see [75,5,7] and related references), and in the theory of homogenization (see [83] and related references).”
Self-improving property of nonlinear higher order parabolic systems near the boundary (2010, background): “For recent parabolic applications of higher integrability in the framework of partial regularity and Calder ónZygmund type estimates, see for example Acerbi-Mingione [4], Acerbi-MingioneSeregin [5], B̈ogelein [10], Duzaar-Mingione [16], Duzaar-Mingione-Steffen [17] and B̈ogelein-Duzaar-Mingione [11]”
Second order parabolic systems, optimal regularity, and singular sets of solutions (2005, methodology): “On the other hand, recently, non-a-priori regular solutions have been considered, b assuming more regularity of A with respect to the “coefficients” (x, t) and, in particular, no dependence on variableu [38,1]; the methods of this last paper are suited for systems with growth conditions more gene th”
Gradient estimates for the p (x)-Laplacean system (2005, background): “Therefore a great deal of work has been developed around variational and elliptic problems with ‘‘pðxÞgrowth’’ that is, involving the energy (2); see also [3], [4] and related references.”
A strong maximum principle for differential equations with nonstandard p(x)-growth conditions (2005, methodology): “There are already some results about this kind of problems (see [1–13,15–20,22,24,25]).”
Existence of solutions to an initial Dirichlet problem of evolutional p(x)-Laplace equations☆ (2012, background): “The typical case is the so-called evolution p-Laplace equation with exponent p as a function of the external electromagnetic field (see [1,2,10] and the references therein).”
Regularity of minima: An invitation to the dark side of the calculus of variations (2006, methodology): “Originally developed in a variational context, such methods were adapted, and extended to approach more general problems [7, 10].”
Hölder estimates for parabolic p(x, t)-Laplacian systems (2012, background): “For simplified versions of this model partial regularity results can be found in [2,19].”
The boundary regularity of non-linear parabolic systems I (2010, background): “In the interior this can be achieved by using the system and the weak differentiability of Du with respect to x (see for instance [2,6,18]).”