On exact analytical solutions of equations of Maxwell incompressible viscoelastic medium
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S. V. Meleshko
Abstract
The presentation (03 June 2020) is based on several of our papers related with two-dimensional flows near a free critical point of an incompressible viscoelastic Maxwell medium with upper, lower, and corotational convective derivatives with the rheological constitutive law. It is performed by way of a complete compatibility analysis. The two solutions found are already known as substantially new solutions. Nonsingular solutions of the stress tensor at the critical point and bounded at infinity are constructed. Exact analytical formulae for the stress tensor were obtained.
Abstract
The presentation (03 June 2020) is based on several of our papers related with two-dimensional flows near a free critical point of an incompressible viscoelastic Maxwell medium with upper, lower, and corotational convective derivatives with the rheological constitutive law. It is performed by way of a complete compatibility analysis. The two solutions found are already known as substantially new solutions. Nonsingular solutions of the stress tensor at the critical point and bounded at infinity are constructed. Exact analytical formulae for the stress tensor were obtained.
Chapters in this book
- Frontmatter I
- Preface V
- Contents VII
- About the editors IX
- List of contributors XI
- Intermediate systems and invariants 1
- Folding in fluids 19
- Vortex models of plane turbulent flows 37
- Equations of dyon electromagnetic field 53
- Minimal action principle for gravity and electrodynamics, Einstein lambda, and Lagrange points 65
- Methods for constructing invariant conservative finite-difference schemes for hydrodynamic-type equations 83
- On exact analytical solutions of equations of Maxwell incompressible viscoelastic medium 111
- Approximate solution of a boundary-value problem for a model of the far momentumless turbulent wake 125
- Analysis of overdetermined system that describes the special class of two-dimensional motion of an ideal fluid 135
- Discrete orthogonal polynomials: anomalies of time series and boundary effects of polynomial filters 143
- Index 165
Chapters in this book
- Frontmatter I
- Preface V
- Contents VII
- About the editors IX
- List of contributors XI
- Intermediate systems and invariants 1
- Folding in fluids 19
- Vortex models of plane turbulent flows 37
- Equations of dyon electromagnetic field 53
- Minimal action principle for gravity and electrodynamics, Einstein lambda, and Lagrange points 65
- Methods for constructing invariant conservative finite-difference schemes for hydrodynamic-type equations 83
- On exact analytical solutions of equations of Maxwell incompressible viscoelastic medium 111
- Approximate solution of a boundary-value problem for a model of the far momentumless turbulent wake 125
- Analysis of overdetermined system that describes the special class of two-dimensional motion of an ideal fluid 135
- Discrete orthogonal polynomials: anomalies of time series and boundary effects of polynomial filters 143
- Index 165
