The structure of solutions near a sonic line in gas dynamics via the pressure gradient equation (Q298100)
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scientific article; zbMATH DE number 6595410
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The structure of solutions near a sonic line in gas dynamics via the pressure gradient equation |
scientific article; zbMATH DE number 6595410 |
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The structure of solutions near a sonic line in gas dynamics via the pressure gradient equation (English)
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20 June 2016
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existence
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two-dimensional Riemann problem
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sonic line
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characteristic analysis
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weighted metric
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fixed point
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The purpose of this paper is to study the two dimensional pressure gradient equation NEWLINE\[NEWLINE\begin{cases} u_t+p_x=0 \\v_t+p_y=0 \\p_t+pu_x+pv_y=0. \end{cases} \eqno{(1)}NEWLINE\]NEWLINE The first theorem states that there is a classic solution to (1) in the so-called hyperbolic region, which satisfies certain boundary conditions. Another theorem states that there is a classic solution to (1) for new coordinates in a certain strong domain.NEWLINENEWLINEThe proofs use Lipschitz continuity and Cauchy sequences.
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