Unsteady flows of non-Newtonian fluids in generalized Orlicz spaces

Fractional order Orlicz-Sobolev spaces

“…In this context we prove a Bourgain -Brezis -Mironescu type formula for functions in this space as well as for sequences of functions. Finally, we deduce some consequences such as the Γ−convergence of modulars and convergence of solutions for some non-local magnetic Laplacian allowing non-standard growth laws to its local counterpart.On the other hand, when studying phenomena allowing behaviors more general than power laws, such as anisotropic fluids with flows obeying nonstandard rheology [8,17] or capillarity phenomena, 2010 Mathematics Subject Classification. 46E30, 35R11, 45G05.…”

“…On the other hand, when studying phenomena allowing behaviors more general than power laws, such as anisotropic fluids with flows obeying nonstandard rheology [8,17] or capillarity phenomena, 2010 Mathematics Subject Classification. 46E30, 35R11, 45G05.…”

A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces

“…in [42,129]. We refer also to [107,108,110,111,196,197] for some developments arising around the theory of non-Newtonian fluids and for existence to some parabolic problems within the setting to [183,184]. Nowadays intensively investigated fields are also potential theory [115], harmonic analysis [72,121], regularity theory [116,120], and homogenization within the setting is studied in [39,40].…”

Unsteady flows of heat-conducting non-Newtonian fluids in Musielak–Orlicz spaces

“…In order to formulate the growth conditions of the stress tensor we use general convex function M called an N -function similarly as in [19,20,45,46] (for a definition see Section 2.1). We assume that stress tensor S S S : Ω × R + × R + × R 3×3 sym → R 3×3 sym satisfies (R 3×3 sym stands for the space of 3 × 3 symmetric matrices): S1.…”

“…But then it may appear that the standard growth conditions, i.e. |S S S(D D D, E)| ≤ c(1 + |D D D|) p−1 , S S S(D D D, E) : D D D ≥ c|D D D| p (E denotes electric flux) are not satisfied, because the tensor S S S may possess the growth of different powers in various directions of D D D (for the example see also [46]).…”