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

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
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