Remark on cavitation solutions of stationary compressible Navier-Stokes equations in one dimension. (English) Zbl 0763.35074

Lovicar, Vladimír; Straškraba, Ivan

Czech. Math. J. 41(116), No. 4, 653-662 (1991).

Summary: The author investigates the cavitation solutions to the stationary compressible Navier-Stokes equations in one dimension \[ p(\rho)_ x=\rho f,\quad x\in(0,1),\qquad\int^ 1_ 0\rho(x)dx=1,\quad \rho(x)\geq 0,\quad x\in (0,1), \] where \(p\in C^ 1((0,\infty))\), \(p(0+)=p(0)=0\), \(p'(r)>0\) for \(r>0\), \(f=f(x)\), \(f\in L^ \infty(0,1)\).
Some examples and existence theorems of this problem are given.

MSC:

35Q30	Navier-Stokes equations
76N10	Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35A05	General existence and uniqueness theorems (PDE) (MSC2000)

Keywords:

solutions with vacuum states; examples

References:

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