Regularity and Expansion for Steady Prandtl Equations

Abstract

Due to degeneracy near the boundary, the question of high regularity for solutions to the steady Prandtl equations has been a longstanding open question since the celebrated work of Olenick. We settle this open question in affirmative in the absence of an external pressure. Our method is based on energy estimates for the quotient, $q=\frac{v}{\bar{u}}$, $\bar{u}$ being the classical Prandtl solution, via the linear Derivative Prandtl Equation (LDP). As a consequence, our regularity result leads to the construction of Prandtl layer expansion up to any order.

arXiv commentaccepted version. arXiv admin note: text overlap with arXiv:1805.05891

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Cited by in corpus (2)

• Well-posedness of the MHD boundary layer system in Gevrey function space without Structural Assumption
• Global $C^{\infty }$ Regularity of the Steady Prandtl Equation