• 作者： 林琦焜
• 作者服務機構： 國立成功大學數學系暨應用數學研究所
• 中文摘要： 此文主要是探討Navier-Stokes方程之消散極限(dissipation limit)。我們利用Navier-Stokes方程的渦流表現式(vorticity formulation)得到一些精確解(exact solutions)並且藉由Young's測度來討論其消散極限(dissipation limit)，同時也探討Hopf-Cole關於Burgers'方程的解，我們發現不必用compensated compactness與method of steepest descent而由Radon-Nikodym定理直接可研究其消散極限，當然這些都完全依賴於其精確解。
• 英文摘要： Based on the vorticity formulation of the Navier-Stokes equations, some exact solutions are obtained.We discuss their dissipation limit using the language of the weak limit through the Young's measure·The classical Hopf-Cole solution of the viscous Burgers’equation and its inviscid (dissipation) limit arealso considered. Instead of the Steepest descent method or compensated compactness argument, we discussthe structure of the singular part of the associated Young's measure and study the inviscid limit by usingthe Radon-Nikodym theorem due to the explicit form of the exact solution.
• 中文關鍵字： Young's measure; Navier-Stokes equations; dissipation
• 英文關鍵字： --