Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On M\'etivier's Lax-Mizohata theorem and extensions to weak defects of
  hyperbolicity. Part two   We continue our study of initial-value problems for fully nonlinear systems
exhibiting strong or weak defects of hyperbolicity. We prove that, regardless
of the initial Sobolev regularity, the initial-value problem has no local $H^s$
solutions, for $s > s_0 + d/2,$ if the principal symbol has a strong, or even
weak, defect of hyperbolicity, and the purely imaginary eigenvalues of the
principal symbol are semi-simple and have constant multiplicity. The index $s_0
> 0$ depends on the severity of the defect of hyperbolicity. These results
recover and extend previous work from G. M\'etivier [{\it Remarks on the well
posedness of the nonlinear Cauchy problem,} 2005], N.Lerner, Y. Morimoto, C.-J.
Xu [{\it Instability of the Cauchy-Kovalevskaya solution for a class of
non-linear systems}, 2010] and N. Lerner, T. Nguyen, B. Texier, {\it The onset
of instability in first-order systems}, 2018]

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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
3
The categories of this paper are: physics
16
The categories of this paper are: stat
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: eess