Article Contents
Article Contents

Zero-electron-mass limit of Euler-Poisson equations

• We study the limit of vanishing ratio of the electron mass to the ion mass (zero-electron-mass limit) in the scaled Euler-Poisson equations. As the first step of this justification, we construct the uniform global classical solutions in critical Besov spaces with the aid of Shizuta-Kawashima" skew-symmetry. Then we establish frequency-localization estimates of Strichartz-type for the equation of acoustics according to the semigroup formulation. Finally, it is shown that the uniform classical solutions converge towards that of the incompressible Euler equations (for ill-preparedinitial data) in a refined way as the scaled electron-mass tends to zero. In comparison with the classical zero-mach-number limit in [7,23], we obtain different dispersive estimates due to the coupled electric field.
Mathematics Subject Classification: Primary: 35B25, 35L45; Secondary: 35M20.

 Citation:

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