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arXiv · 1403.0791

On the well-posedness of higher order viscous Burgers' equations

Xavier Carvajal·Mahendra Panthee
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Abstract

We consider higher order viscous Burgers' equations with generalized nonlinearity and study the associated initial value problems for given data in the $L^2$-based Sobolev spaces. We introduce appropriate time weighted spaces to derive multilinear estimates and use them in the contraction mapping principle argument to prove local well-posedness for data with Sobolev regularity below $L^2$. We also prove ill-posedness for this type of models and show that the local well-posedness results are sharp in some particular cases viz., when the orders of dissipation $p$, and nonlinearity $k+1$, satisfy a relation $p=2k+1$.

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Xavier Carvajal, Mahendra Panthee. 2014-03-04. On the well-posedness of higher order viscous Burgers' equations. https://arxiv.org/abs/1403.0791

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