vladimir onoprienko edited begin_equation_2_begin_align__.tex  about 8 years ago

Commit id: cd8ceb941df6c3ed40a7566b692301061ce790f6

deletions | additions      

       

u \frac{\partial u}{\partial x}   \to  \frac{\partial}{\partial y} \left( u \frac{\partial u}{\partial x}\right)   &= =  \frac{\partial u}{\partial y} \cdot \frac{\partial u}{\partial x} + u \frac{\partial^2 u}{\partial x \partial y} = &=  \frac{\partial}{\partial y}\left[ \left( - \frac{\partial \zeta}{\partial y} \right) \cdot \frac{\partial}{\partial x} \left( -\frac{\partial \zeta}{\partial y} \right) \right] = \\ %newline   &= \frac{\partial^2 \zeta}{\partial y^2} \cdot \frac{\partial^2 \zeta}{\partial x \partial y }   + \frac{\partial \zeta}{\partial y } \cdot \frac{\partial^3 \zeta}{\partial x \partial y^2}\\