在這篇研究報告中，我們仔細檢視了 P.L. Lions [Lio98] 與 E. Feireisl [FNP01] 對可壓縮等熵 Navier-Stokes 方程組弱解整體存在性的證明。Lions [Lio98] 證明了在三維空間中，當熱容比大於 9/5，而且初值所對應的動能與位能是有限的，則方程組的弱解在任意時間內都存在。之後，Feireisl把 Lions 的結果推廣到熱容比大於 3/2 的情形。本文按 E. Feireisl [FNP01] 與 A. Novotny [NS04] 的證明方式，試著給予一個比較詳細的過程。

Abstract In this survey artical, we scrutinize the paper by P.L. Lions [Lio98] and E. Feireisl [FNP01] that contribute to the global in time existence of solutions for the compressible isentropic Navier-Stokes equations. If initial data has finite energy, Lions obtained global existence of weak solutions when the adiabatic constant gamma>9/5 . The result was later improved by Feireisl for gamma>3/2. This artical is intended to give some more details about the proofs of the global in time existence by E. Feireisl [FNP01] and A. Novotny [NS04].

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