1. In mathematics and functional analysis, solutions to differential equations that satisfy the equation in an integral or distributional sense rather than pointwise, allowing for less regularity and differentiability.
The Navier-Stokes equations often require weak solutions to be well-defined for turbulent flows.
As equações de Navier-Stokes frequentemente requerem soluções fracas para serem bem definidas em escoamentos turbulentos.
2. Solutions that may not be differentiable everywhere but still satisfy the equation when tested against smooth test functions.
Weak solutions allow for the treatment of non-smooth initial conditions in partial differential equations.
Soluções fracas permitem o tratamento de condições iniciais não-suaves em equações diferenciais parciais.