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NCTS Nonlinear PDE and Analysis Seminar
14:30 - 15:30, October 27, 2021 (Wednesday)
Cisco Webex, Online seminar
(線上演講 Cisco Webex)
On Strong Convergence of a Modified Elliptic Regularization to Advection Equations (II)
Daisuke Kawagoe (Kyoto University)


We consider an advection equation with the homogeneous inflow boundary condition in a bounded domain with the piecewise $C^1$ boundary. When we apply the standard elliptic regularization to this boundary value problem, its convergence rate as the viscosity parameter $\epsilon$ tends to $0$ is of order $\epsilon^{1/4}$ in some cases and not known in general. In this talk, we show that a family of solutions obtained by a modified elliptic regularization converges to the solution to the original problem with order $\epsilon^{1/2}$ under the assumption that the original solution has $H^1$ regularity. We also derive better convergence rates with more assumptions on domains, vector fields, and regularity of the original solution.


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