Abstract
We study the Cauchy problem for a system of one-dimensional viscous conservation laws with rotational invariance, \(\displaystyle \mathbf {u}_{t} + \left[ \;\!|\mathbf {u}|^{2}\mathbf {u}\;\!\right] _{x} = \mathbf {u}_{xx}\),with the aim of deriving some a priori estimates for various \(L^{p}\) norms of its solutions through a direct method.
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