instituto de matemáticas universidad de sevilla
Antonio de Castro Brzezicki
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Well-posedness for some dispersive perturbations of Burger’s equation
Conversaciones Fluidas

Abstract: We show that the Cauchy problem associated to a class of dispersive perturbations of Burgers’ equations containing the low dispersion Benjamin-Ono equation

 

$\delta_{t}u - D_{x}^{\alpha} \delta_{x}u + u\delta_{x}u = 0$

 

 

with $0 < \alpha \leq 1$, is locally well-posed in $H^s (R$) for $s > s_{\alpha} := \frac{3}{2} - \frac{5\alpha}{4}$.

As a consequence, we obtain global well-posedness in the energy space $H^{\frac{\alpha}{2}}(R)$ as soon as $\frac{\alpha}{2} > s_{\alpha}$, i.e. $\alpha > \frac{6}{7}$.


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