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We study the Cauchy problem of the quasilinear evolution equations in -spaces. Based on the theories of maximal -regularity of sectorial operators, interpolation spaces, and time-weighted -spaces, we establish the local posedness for a class of abstract quasilinear evolution equations with lower regular initial data. To illustrate our results, we also deal with the second-order parabolic equations and the Navier-Stokes equations in -spaces with temporal weights.

journal of function spaces

Quasilinear Evolution Equations in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>μ</mml:mi></mml:mrow><mml:mrow><mml:mi>P</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:math>-Spaces with Lower Regular Initial Data

Quasilinear Evolution Equations in LμP-Spaces with Lower Regular Initial Data