Global solutions to the 3-D incompressible inhomogeneous Navier–Stokes system
By Marius Paicu, Ping Zhang. 2012
145 citations recorded by the source corpus.
In this paper, we consider the global well-posedness of the 3-D incompressible inhomogeneous Navier–Stokes equations with initial data in the critical Besov spaces a0∈Bq,13q(R3), u0=(u0h,u03)∈Bp,1−1+3p(R3) for p, q satisfying 1<q⩽p<6 and 1q−1p⩽13. More precisely, we prove that there exist two positive constants c0, C0 such that if (μ‖a0‖Bq,13q+‖u0h‖Bp,1−1+3p)exp(C0‖u03‖Bp,1−1+3p2/μ2)⩽c0μ, then (1.3) has a unique global solution a∈L˜∞(R+;Bq,13q(R3)), u∈L˜∞(R+;Bp,1−1+3p(R3))∩L1(R+;Bp,11+3p(R3)). In particular, this result implies the global well-posedness result in Abidi and Paicu (2007) [2] for the inhomogeneous Navier–Stokes system with small initial data.
Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/8abab5d98655eedc483e014f18c41f3a5c8850b9
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In Applied Mathematics
In Computational Mechanics
In Mathematical Physics
Citations in the corpus
- Global well-posedness for the incompressible Navier–Stokes equations with density-dependent viscosity coefficient (2015, background): “1) with small initial data belonging to certain scale invariant spaces were obtained in [1,2,8,20] and many others.”
- Global Unique Solvability of Inhomogeneous Navier-Stokes Equations with Bounded Density (2013, background): “Paicu and Zhang [18] further extended the well-posedness result in [2] so that even if one component of the initial velocity is large, (1.”