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Smooth Solutions and the Equations of Incompressible Fluid Flow

  • A. Majda
Chapter
Part of the Applied Mathematical Sciences book series (AMS, volume 53)

Abstract

Here we study several topics related to the existence of smooth solutions for the general system of conservation laws,
$$ \frac{{\partial u}}{{\partial t}} + \sum\limits_{j = 1}^N {\frac{\partial }{{\partial {x_j}}}{\mkern 1mu} {F_j}(u){\mkern 1mu} = {\mkern 1mu} S(u,x,t)} $$
(2.la)
with the smooth initial data
$$ {\text{u(x,0) = }}{{\text{u}}_0}{\text{(x)}} $$
(2.lb)
where u0(x) ∈ G1, \( {{\bar G}_1} \subset \subset G \) for all x ∈ RN. We always assume the detailed structure of a symmetric hyperbolic system as described in (1.17). This chapter has three main subsections which we describe briefly below.

Keywords

Mach Number Smooth Solution Local Existence Compressible Fluid Singular Limit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1984

Authors and Affiliations

  • A. Majda
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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