Navier-Stokes Equations and Related Nonlinear Problems

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This collection explores various advanced topics in fluid dynamics and mathematical analysis, focusing on the Navier-Stokes equations and related systems. It begins with an examination of exponential decay problems associated with these equations, followed by discussions on the existence of solutions for non-stationary second-grade fluids. Numerical simulations for shallow lakes are presented, alongside semi-implicit schemes for nonlinear Schrödinger-type equations. Key themes include surface diffusion flow, domain functionals, and the stabilization of the inf-sup condition, with computations of pressure included. The work addresses time-periodic problems for Navier-Stokes equations with nonstandard boundary conditions and the role of Orlicz spaces in global existence issues for multidimensional compressible fluids with nonlinear viscosity. Further analysis covers stability and uniqueness for second-grade fluids with permeable boundaries, regularity techniques for nonlinear Stokes-like elliptic systems, and stationary Boussinesq equations under general outflow conditions. The collection also investigates two-layer flows in unbounded domains, compressible Stokes flow driven by capillarity, and weighted Dirichlet problems in strongly degenerate elliptic systems. Additional topics include finite difference methods for sessile drop equations, stability properties of Boussinesq equations, and open boundary problems for inviscid