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Huang, Bingyuan; Ding, Shijin; Wen, Huanyao

Local classical solutions of compressible Navier-Stokes-Smoluchowski equations with vacuum. (English) Zbl 1356.35160

Discrete Contin. Dyn. Syst., Ser. S 9, No. 6, 1717-1752 (2016).
Summary: This paper is concerned with the Cauchy problem for compressible Navier-Stokes-Smoluchowski equations with vacuum in \(\mathbb{R}^3\). We prove both existence and uniqueness of the local strong solution, and then obtain a local classical solution by deriving the smoothing effect of the strong solution for \(t>0\).

Cited in 1 Review
Cited in 19 Documents

MSC:

35Q30 Navier-Stokes equations
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
35D35 Strong solutions to PDEs
76T20 Suspensions

Keywords:

classical solution; compressible Navier-Stokes-Smoluchowski equations; vacuum
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References:

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