Semi-linearized compressible Navier-Stokes equations perturbed by noise. (English) Zbl 1014.35074

Bessaih, Hakima

Electron. J. Differ. Equ. 2003, Paper No. 02, 18 p. (2003).

Summary: We consider the following system of equations with a stochastic perturbation \[ \overline\rho u_t+\nabla p(\rho)=\mu\Delta u+(\mu+\lambda)\nabla\text{div} u +G_t\text{ in }Q_T, \]
\[ \rho_t +\text{div}(\rho u)=0\text{ in }Q_T, \] where \(Q_T=(0,T)\times D\), \(D=(0,1)^2\), \(\overline\rho,\lambda,\mu\) are constants such that \(\overline\rho >0\), \(\mu>0\), \(\mu+\lambda\geq 0\); while \(G\) is a stochastic process in a function space. We prove the existence and uniqueness of solutions in a class of potential flows.

MSC:

35Q30	Navier-Stokes equations
76N10	Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35R60	PDEs with randomness, stochastic partial differential equations

Keywords:

existence; uniqueness