Chapter 1: Condensate growth term: existence, uniqueness, propagations of moments

Chapter 2: Uniform in time lower bound for solutions to a quantum Boltzmann equation of bosons

Chapter 3: What else besides the condensate growth term?

Chapter 6: Derivation of quantum kinetic equations

Chapter 7: Coupling kinetic and Schrodinger equations

Chapter 8: Quantum hydrodynamic approximations to finite temperature trapped Bose gases

Chapter 9: Wave turbulence theory for capillary water waves

Chapter 10: On the wave turbulence theory for stratified flows in the ocean

Chapter 11: Optimal local well-posedness theory for the kinetic wave equation.

Chapter 12: On the energy cascade of acoustic wave turbulence: Beyond Kolmogorov-Zakharov solutions

Chapter 13: A reaction network approach to the theory of acoustic wave

turbulence

**EXTRA CHAPTERS: SCIENTIFIC COMPUTING-COMPUTATIONAL SCIENCES and UNCERTAINTY QUANTIFICATION-SENSITIVITY ANALYSIS**

Extra Chapter 1: iHDG – Iterative Hybridized Discontinuous Galerkin method

Extra Chapter 2: iHDG – Iterative Hybridized Discontinuous Galerkin method (Part 2)