Hyperbolic Conservation Laws

By Mathematisches Forschungsinstitut Oberwolfach, C. Dafermos, Randy LeVeque. 2004

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Vanishing viscosity limit of the Navier‐Stokes equations to the euler equations for compressible fluid flow (2009, methodology): “s as viscous gases with vanishing real physical viscosity can date back the seminal paper by Stokes [30] and the important contribution of Rankine [26], Hugoniot [15], and Rayleigh [27] (cf. Dafermos [8]). However, the ﬁrst rigorous convergence analysis of vanishing physical viscosity from the Navie”
An ill posed Cauchy problem for a hyperbolic system in two space dimensions (2003, background): “ace dimensions the Cauchy problem can be ill posed. The systems on IRm that we consider take the special form ∂ ∂t ui + Xm α=1 ∂ ∂xα fα |u| ui = 0 i = 1,...,n. (1.1) For physical motivations, see [2] or [5]. Given a suﬃciently regular initial condition u(0,x) = ¯u(x), (1.2) the solution of the Cau”
On Nonlinear Stochastic Balance Laws (2011, methodology): “ analysis of nonlinear stochastic balance laws. When σ≡ 0, (1.1) becomes a nonlinear conservation law for which the maximum principle holds. A satisfactory well-posedness theory is now available (cf. [5]). In [10], a one-dimensional stochastic balance law was analyzed for u0 in L∞ and compactly supp”