Preface -- List of contributing authors -- 1 Equations of fluid motion -- 1.1 Basic hypotheses of continuum -- 1.2 Two methods for the continuum description. Translation formula -- 1.3 Integral conservation laws. Equations of continuous motion -- 1.4 Thermodynamics aspects -- 1.5 Classical models of liquids and gases -- 2 Conditions on the interface between fluids and on solid walls -- 2.1 Notion of the interface -- 2.2 Kinematic condition -- 2.3 Dynamic condition -- 2.4 Elements of thermodynamics of the interface -- 2.5 Conditions of continuity -- 2.6 Energy transfer across the interface -- 2.7 Free surfaces -- 2.8 Additional conditions -- 3 Models of convection of an isothermally incompressible fluid -- 3.1 Isothermally incompressible fluid -- 3.2 Equations of thermal convection of an isothermally incompressible fluid -- 3.3 Model of linear thermal expansion -- 3.4 Some submodels -- 3.5 On boundary conditions -- 3.6 Two problems of convection -- 4 Hierarchy of convection models in closed volumes -- 4.1 Initial relations -- 4.2 Similarity criteria -- 4.3 Transition to dimensional variables -- 4.4 Expansion in the small parameter -- 4.5 Equations of microconvection of an isothermally incompressible fluid -- 4.6 Oberbeck-Boussinesq equations -- 4.7 Linear model of the transitional process -- 4.8 Some conclusions -- 4.9 Convection of nonisothermal liquids and gases under microgravity conditions -- 4.10 Convection of a thermally inhomogeneous weakly compressible fluid -- 4.11 Exact solutions in an infinite band -- 4.12 Analysis of well-posedness of the initial-boundary problem for equations of convection of a weakly compressible fluid -- 5 Invariant submodels of microconvection equations -- 5.1 Basic model and its group properties -- 5.2 Optimal subsystems of the subalgebras Θ1 and Θ2, factor-systems, and some solutions.

5.3 On one steady solution of microconvection equations in a vertical layer -- 5.4 Solvability of a nonstandard boundary-value problem -- 5.5 Unsteady solution of microconvection equations in an infinite band -- 5.6 Invariant solutions of microconvection equations that describe the motion with an interface -- 6 Group properties of equations of thermodiffusion motion -- 6.1 Lie group of thermodiffusion equations -- 6.2 Group properties of two-dimensional equations -- 6.3 Invariant submodels and exact solutions of thermodiffusion equations -- 7 Stability of equilibrium states in the Oberbeck-Boussinesq model -- 7.1 Convective instability of a horizontal layer with oscillations of temperature on the free boundary -- 7.2 Instability of a liquid layers with an interface -- 7.3 Convection in a rotating fluid layer under microgravity conditions -- 8 Small perturbations and stability of plane layers in the microconvection model -- 8.1 Equations of small perturbations -- 8.2 Stability of the equilibrium state of a plane layer with solid walls -- 8.3 Emergence of microconvection in a plane layer with a free boundary -- 8.4 Stability of a steady flow in a vertical layer -- 9 Numerical simulation of convective flows under microgravity conditions -- 9.1 Numerical methods used for calculations -- 9.2 Numerical study of unsteady microconvection in canonical domains with solid boundaries -- 9.3 Numerical study of steady microconvection in domains with free boundaries -- 9.4 Study of convection induced by volume expansion -- 9.5 Convection in miscible fluids -- 10 Convective flows in tubes and layers -- 10.1 Group-theoretical nature of the Birikh solution and its generalizations -- 10.2 An axial convective flow in a rotating tube with a longitudinal temperature gradient.

10.3 Unsteady analogs of the Birikh solutions -- 10.4 Model of viscous layer deformation by thermocapillary forces -- Bibliography -- Index.