Biography
Prof. Matania Ben-Artzi
Prof. Matania Ben-Artzi
Hebrew University of Jerusalem, Israel
Title: Conservation laws on the sphere: From Shallow-Water to Burgers
Abstract: 

One of the best known models for atmospheric flow is that of the "Shallow-Water" system (on the sphere). It is a complicated system of nonlinear hyperbolic equations, involving material discontinuities, shocks and other wave patterns. The first part of this talk is devoted to a Lagrangian derivation of the system. 

In the second part a scalar conservation law is introduced. It is the "geometric" equivalent of the famous Burgers equation. The theory of existence and uniqueness is stated (uniqueness is implied by a suitable version of the entropy condition). The proofs (not discussed in detail in this talk) use a combination of dissipative estimates and Young measures. Some numerical results are presented, showing a very rich collection of steady-state solutions, solutions confined to designated domains and more. 

(Joint work with J. Falcovitz and Ph. LeFloch).

Biography: 
Matania Ben-Artzi is a Professor of Mathematics at the Hebrew University of Jerusalem. His research extends both to pure and applied mathematics. The three main areas of interest are: 1) Spectral theory of partial differential operators, as reflected in the book: M. Ben-Artzi and A. Devinatz, “The Limiting Absorption Principle for Partial Differential Operators” (Amer. Math. Soc. 1987). 2) Nonlinear hyperbolic equations (conservation laws) including numerical aspects, as reflected in the book: M. Ben-Artzi and J. Falcovitz, “Generalized Riemann Problems in Computational Fluid Dynamics” (Cambridge Univ. Press, 2003). 3) Navier-Stokes equations including numerical aspects, as reflected in the book: M. Ben-Artzi, J.-P. Croisille and D. Fishelov, “Navier-Stokes Equations in Planar Domains” (Imperial College Press, 2013).