Geodesic
Initial-boundary value problem with a~free surface condition for the modified Navier--Stokes equations
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 25, Tome 213 (1994), pp. 93-115

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In this paper we study the global classical solvability on the semiaxis $t\in\mathbb R^+$ of the second initial-boundary value problem with a free surface condition (0.1) for other modified Navier–Stokes equations: Ladyzhenskaya's equations (0.3), equations of Jeffrey–Oldroyd fluids (0.4), equations of Kelvin–Voight fluids (0.5) and equations of aqueous solutions of polymers (0.6). Bibliography: 31 titles. 
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     author = {A. P. Oskolkov},
     title = {Initial-boundary value problem with a~free surface condition for the modified {Navier--Stokes} equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {93--115},
     publisher = {mathdoc},
     volume = {213},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_213_a5/}
}
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A. P. Oskolkov. Initial-boundary value problem with a~free surface condition for the modified Navier--Stokes equations. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 25, Tome 213 (1994), pp. 93-115. http://geodesic.mathdoc.fr/item/ZNSL_1994_213_a5/