Geodesic
Existence of Global Solutions to Multidimensional Equations for Bingham Fluids
Matematičeskie zametki, Tome 82 (2007) no. 4, pp. 560-577

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We consider equations describing the multidimensional motion of compressible viscous (non-Newtonian) Bingham-type fluids, i.e., fluids with multivalued function relating the stresses to the tensor of strain rates. We prove the global existence theorem in time and in the initial data for the first initial boundary-value problem corresponding to flows in a bounded domain in the class of “weak” generalized solutions. In this case, we admit an anisotropic relation between the stress and strain rate tensors and study admissible relations of this kind in detail.
Keywords: compressible viscous (non-Newtonian) Bingham-type fluid, global existence theorem, initial boundary-value problem, weak generalized solution, Orlicz space. 
@article{MZM_2007_82_4_a10,
     author = {A. E. Mamontov},
     title = {Existence of {Global} {Solutions} to {Multidimensional} {Equations} for {Bingham} {Fluids}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {560--577},
     publisher = {mathdoc},
     volume = {82},
     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_4_a10/}
}
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A. E. Mamontov. Existence of Global Solutions to Multidimensional Equations for Bingham Fluids. Matematičeskie zametki, Tome 82 (2007) no. 4, pp. 560-577. http://geodesic.mathdoc.fr/item/MZM_2007_82_4_a10/