Boundary Value Problems in Mechanics of Nonhomogeneous Fluids (eBook)

Cover 1
TOC$Contents 10
Preface 6
CH$Chapter 1. Models of the Synamics of Heterogeneous Media and the Body of Mathematics 14
1. Models of mechanics of heterogeneous fluids 14
2. Auxiliary information from analysis and differential equations 33
CH$Chapter 2. Correctness "In The Whole" Of The Boundary Problems For Equations Of One-Dimensional Non-Stationary Motion Of A Viscous Gas 52
1. Formulation of the basic boundary problem. Lagrange variables 52
2. Auxiliary constructions 56
3. Estimates for density and temperature from above and below 61
4. A priori estimates for derivatives 65
5. Proof of the theorem of existence and uniqueness 73
6. The Cauchy problem 81
7. Other boundary value problems 88
8. Stabilization of solutions under infinite time increase 99
9. Unsolved problems 109
CH$Chapter 3. Initial-Boundary Value Problems For The Navier-Stokes Equations Of Nonhomogeneous Viscous Incompressible Fluid 114
1. The existence of generalized solutions 114
2. Differential properties of the generalized solutions 126
3. Unilateral boundary problems 140
4. A model of an inhomogeneous fluid with diffusion 152
5. Model of a medium with intrinsic degrees of freedom 156
6. Problems unsolved 160
CH$Chapter 4. Correctness Of The Problem Of Flow Through An Ideal Incompressible Liquid 162
1 Formulation of the problem and the basic result 162
2. Equivalent formulations of the boundary problem 166
3. The method of successive approximations 175
4. A priori estimates 185
5. Proof of the existence and the uniqueness of the solution 197
6. Some generalizations of the basic theorem 200
7. Unsolved problems 208
CH$Chapter 5. Filteration of Immiscible liquids 212
1. Reduction of equations, formulation of problem 212
2. Determination of generalized solutions. Problem regulariz-ation, maximum and compactness principles 216
3. The theorem of existence of generalized solutions 225
4. Determination of the summed velocity of inhomogeneous liquid filtration 233
5. On distribution of phase saturation on a given field of a summed filtration velocity 243
6. On a joint problem 255
7. Stationary problem 259
8. Further smoothness of regular non-stationary problem solutions 265
9. Degenerating non-stationary problem 280
10. Approximation solution of two-phase filtration problems 302
11. Unsolved problems 306
References 310