In the past, the structural optimization of design problems considering viscous fluid flow has been accomplished using a variety of methods.Fluid problems were first optimized using shape optimization methods based on equilibrium equations such as the Stokes and Navier-Stokes equations.However, such methods were hampered by poor design flexibility because shape optimization only considers movement of the fluid/solid boundaries in the intended design domain, and the creation of new holes in the design domain is not allowed, so the results strongly depend on the initial configuration.Thus, topology optimization, which enables the creation of new holes during the optimal process, was naturally applied to fluid problems.Although topology optimization allows greater design flexibility than shape optimization does, the expression of clear boundaries in the optimal structure typically requires the application of an appropriate filtering scheme.Structural optimization methods based on level set boundary expressions have been applied more widely recently, because the use of the scalar level set function inherently enables the expression of clear boundaries.However, level set-based methods are typically considered shape optimization methods and have poor design flexibility due to the use of the Hamilton-Jacobi equation when updating the level set function, which blocks the creation of new holes in the optimal structure during the optimization process.On the other hand, the Navier-Stokes equation must be used as an equilibrium equation when performing structural optimization that considers viscous fluid flow.The Navier-Stokes equation has a nonlinear term, so its numerical solutions tend to show poor convergence.Although the Stokes equation that neglects the convection term is stably able to obtain numerical solutions, its adaptability to realistic fluid flow is limited to low Reynolds number fields (Re < 1).To overcome the above problems, this paper proposes a topology optimization method incorporating level set boundary expressions based on the concept on the phase field method, under the Oseen equilibrium equation, which we apply to a minimum flow friction problem.The Oseen equation is a simplified equilibrium equation in which the nonlinear term is replaced with a linear term, guaranteeing good convergence of the numerical solutions.Using a reaction-diffusion equation to update the level set function, we construct a new topology optimization method for the Oseen flow problem which is able to create new holes and maintain clear boundaries during the optimization process.To demonstrate the usefulness of our method, we obtained optimal structures of flow channels for an internal Oseen flow problem.Comparison of the optimal structures obtained using the Oseen equation with those obtained via the Stokes equation revealed that only the Oseen equation provided appropriately different optimal structures in response to Reynolds number variation.