Courant Institute of Mathematical Sciences

About: Courant Institute of Mathematical Sciences is a education organization based out in New York, New York, United States. It is known for research contribution in the topics: Nonlinear system & Boundary value problem. The organization has 2414 authors who have published 7759 publications receiving 439773 citations. The organization is also known as: CIMS & New York University Department of Mathematics.

Polynya dynamics: A review of observations and modeling

Abstract: [1] Polynyas are nonlinear-shaped openings within the ice cover, ranging in size from 10 to 105 km2. Polynyas play an important climatic role. First, winter polynyas tend to warm the atmosphere, thus affecting atmospheric mesoscale motions. Second, ocean surface cooling and brine rejection during sea ice growth in polynyas lead to vertical mixing and convection, contributing to the transformation of intermediate and deep waters in the global ocean and the maintenance of the oceanic overturning circulation. Since 1990, there has been an upsurge in polynya observations and theoretical models for polynya formation and their impact on the biogeochemistry of the polar seas. This article reviews polynya research carried out in the last 2 decades, focusing on presenting a state-of-the-art picture of the physical interactions between polynyas and the atmosphere-sea ice-ocean system. Observational and modeling studies, the surface heat budget, and water mass transformation within these features are addressed.

The Anelastic Approximation for Thermal Convection

Abstract: A formal scale analysis of the equations of motion in a plane parallel atmosphere is made, assuming conditions to be such that relative fluctuations in density and temperature are small. It is found that an energetically consistent set of approximate equations can be derived which preclude the existence of acoustic motions. Such equations can be used to describe subsonic convection or internal gravity waves. Under certain conditions the analysis can be generalized to include vertical pulsations of the atmosphere.

Existence of solutions for the Ericksen-Leslie system

Abstract: We study the general Ericksen-Leslie system, which describes the flow of liquid crystal materials. The dissipation property of the system is established and is used to prove the global existence of weak solutions. We also study the existence of classical solutions and the asymptotic stability of the solutions.