Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unstable shock formation of the Burgers-Hilbert equation   This paper proves the existence of unstable shocks of the Burgers-Hilbert
equation conjectured in arXiv:2006.05568. More precisely, we construct smooth
initial data with finite $H^9$-norm such that the solution in self-similar
coordinates is asymptotic to the first unstable solution to the self-similar
inviscid Burgers equation. The blowup profile is a cusp with H\"older 1/5
continuity with explicit blowup time and location. Unlike the previously
established stable shocks, the initial data cannot be taken in an open set;
instead, we control the two unstable directions by Newton's iteration.

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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th