| Abstrakt: |
Viscous compressible barotropic motions (described by v‐velocity and ϱ‐density) in a bounded domain Ω ⊂ R 3 with v = 0 on the boundary are considered. Assuming existence of some special global sufficiently regular solutions ( v s ‐velocity and ϱs‐density), we prove their stability by assuming that initial differences of u = v − v s and η=ϱ−ϱs are sufficiently small in some norms. Then we prove existence of u, η such that u,η∈L∞(kT,(k+1)T;H2(Ω)), ut,ηt∈L∞(kT,(k+1)T;H1(Ω)), u∈L2(kT,(k+1)T;H3(Ω)), ut∈L2(kT,(k+1)T;H2(Ω)), where T>0 and k ∈ N ∪ { 0 }. Moreover, u, η are sufficiently small in the above norms. Finally, the existence of global regular solutions such that v = v s + u , ϱ = ϱ s + η is proved. [ABSTRACT FROM AUTHOR] |
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