Titlebook: Equations of Motion for Incompressible Viscous Fluids; With Mixed Boundary Tujin Kim,Daomin Cao Book 2021 The Editor(s) (if applicable) an

BIAS

Fluid Equations,ee kind of bilinear forms for the Stokes and Navier-Stokes equations, variational formulations for the Navier-Stokes problems with mixed boundary conditions and establish the equivalence between the variational formulations and the original PDE problems.

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The Steady Navier-Stokes System,ed, types of boundary conditions under consideration together are different. The variational formulations in Sect. . do not reflect, for example, the boundary conditions for stress and pressure together, but this case is important in practice.

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The Steady Boussinesq System,hlet, Neumann and Robin conditions together. We will get variational formulations consisting of a variational inequality for velocity and a variational equation for temperature, which are equivalent to the original PDE problems for smooth solutions.

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周兴旺

湿润

Albumin

The Non-steady Navier-Stokes System with Friction Boundary Conditions,inequalities obtained in Sect. .. In Sect. . using the results of Sect. ., we get the existence, uniqueness and estimates of solutions to the Navier-Stokes and Stokes problems with the boundary conditions.

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DEAWL

The Steady Equations for Heat-Conducting Fluids,ect. ., we get variational formulations consisting of a variational inequality for velocity and a variational equation for temperature, which are equivalent to the original PDE problems for smooth solutions.

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