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Sharp $H_{x}^{s}$ Ill-posedness of the Hard-sphere Boltzmann Equation
We investigate the ill-posedness mechanism of the hard-sphere Boltzmann equation in $H_{x}^{s}$ Sobolev space. Via a direct construction, we prove a strong-weak type ill-posedness result in the low-regularity regime $s1$ well-posednes
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