Sobolev multipliers,maximal functions and parabolic equations with a quadratic nonlinearity |
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Authors: | Pierre Gilles Lemarié-Rieusset |
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Institution: | LaMME, Univ Evry, CNRS, Université Paris-Saclay, 91025, Evry, France |
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Abstract: | We develop a general framework to describe global mild solutions to a Cauchy problem with small initial values concerning a general class of semilinear parabolic equations with a quadratic nonlinearity. This class includes the Navier–Stokes equations, the subcritical dissipative quasi-geostrophic equation and the parabolic–elliptic Keller–Segel system. |
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Keywords: | 35K57 35B35 Semilinear parabolic equations Morrey spaces Multipliers Hedberg inequality |
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