We study Caccioppoli's inequalities of the non-stationary Stokes equations and Navier-Stokes equations. Our analysis is local near boundary and we prove that, in contrast to the interior case, the Caccioppoli's inequalities of the Stokes equations and the Navier-Stokes equations, in general, fail near boundary.
Bibliographical noteFunding Information:
T. Chang is partially supported by NRF-2017R1D1A1B03033427 and K. Kang is partially supported by NRF-2019R1A2C1084685 and NRF-2015R1A5A1009350.
T. Chang is partially supported by NRF - 2017R1D1A1B03033427 and K. Kang is partially supported by NRF - 2019R1A2C1084685 and NRF - 2015R1A5A1009350 .
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All Science Journal Classification (ASJC) codes
- Applied Mathematics