Geodesic
The solvability of the nonstationary problem for the model system of the barotropic gas flows
Dalʹnevostočnyj matematičeskij žurnal, Tome 2 (2001) no. 1, pp. 37-52

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Considered an approximate system Navier-Stokes equtions for the compressible viscous barotropic flows. The nonpotential flows are considered. The global existence of the weak solutions for the 3-dimensional problem is obtained. In the case the 2-dimensional the theorem of the existense and uniqueness is proved. The proof of main result is based on a new priori estimates. 
@article{DVMG_2001_2_1_a2,
     author = {E. V. Lukina},
     title = {The solvability of the nonstationary problem for the model system of the barotropic gas flows},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {37--52},
     publisher = {mathdoc},
     volume = {2},
     number = {1},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2001_2_1_a2/}
}
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E. V. Lukina. The solvability of the nonstationary problem for the model system of the barotropic gas flows. Dalʹnevostočnyj matematičeskij žurnal, Tome 2 (2001) no. 1, pp. 37-52. http://geodesic.mathdoc.fr/item/DVMG_2001_2_1_a2/