We study the onset of thermal instability with the heat flux prescribed on the fluid boundaries. Assuming Boussinesq fluid, the Landau equation, which describes the evolution of the amplitude of the ...

PNAS is the world's most-cited multidisciplinary scientific serial. It publishes high-impact research reports, commentaries, perspectives, reviews, colloquium papers, and actions of the Academy. In ...

Mathematical theory of hydrodynamic states; energy methods, linear theories, and nonlinear bifurcation theories. Convective, centrifugal, and shear flow instabilities. Instability of unsteady flows ...

Thin liquid films play a crucial role in a wide range of natural and industrial processes, from microfluidic device operation to advanced heat exchanger design. Their behaviour is dictated by the ...