QUANTUM HYDRODYNAMIC EQUATION AND ITS MATHEMATICAL THEORY

Quantum hydrodynamics comes from superfluid, superconductivity, semiconductor and so on. Quantum hydrodynamic model describes Helium II superfluid, Bose–Einstein condensation in inert gas, dissipative perturbation of Hamilton–Jacobi system, amplitude and dissipative perturbation of Eikonal quantum wave and so on. Owing to the broad application of quantum hydrodynamic equations, the study of the quantum hydrodynamic equations has aroused the concern of more and more scholars. Based on the above facts, we collected and collated the data of quantum hydrodynamic equations, and studied the concerning mathematical problems.

The main contents of this book are: the derivation and mathematical models of quantum hydrodynamic equations, global existence of weak solutions to the compressible quantum hydrodynamic equations, existence of finite energy weak solutions of inviscid quantum hydrodynamic equations, non-isentropic quantum Navier-Stokes equations with cold pressure, boundary problem of compressible quantum Euler-Poisson equations, asymptotic limit to the bipolar quantum hydrodynamic equations.

Contents:

• Preface
• The Derivation and Mathematical Models of Quantum Hydrodynamic Equations
• Global Existence of Weak Solutions to the Compressible Quantum Hydrodynamic Equations
• Existence of Finite Energy Weak Solutions of Inviscid Quantum Hydrodynamic Equations
• Non-isentropic Quantum Navier–Stokes Equations with Cold Pressure
• Boundary Problem of Compressible Quantum Euler–Poisson Equations
• Asymptotic Limit to the Bipolar Quantum Hydrodynamic Equations
• References

Readership: For graduate students, doctoral students and researchers who are interested in quantum hydrodynamic equations.

Key Features:

• This book gives some newest results in this field, some of which are deduced by authors and coauthors
• This book will help the readers to sort out issues that are not clarified in previous books and literatures, and enable the readers to carry out basic research with the help of the relevant references when they are interested in specific aspects of the problem