期刊
COMMUNICATIONS IN MATHEMATICAL PHYSICS
卷 216, 期 2, 页码 255-276出版社
SPRINGER
DOI: 10.1007/s002200000322
关键词
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We prove that weak solutions of the Navier-Stokes equations for compressible fluid flow in one space dimension do not exhibit vacuum states, provided that no vacuum states are present initially. The solutions and external forces that we consider are quite general: the essential requirements are that the mass and energy densities of the fluid be locally integrable at each time, and that the L-loc(2)-norm of the velocity gradient be locally integrable in time. Our analysis shows that, if a vacuum state were to occur, the Viscous force would impose an impulse of infinite magnitude on the adjacent fluid, thus violating the hypothesis that the momentum remains locally finite.
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