Strong solutions to the nonlinear heat equation in homogeneous Besov spaces Original Research Article

In this paper we study the Cauchy problem of the nonlinear heat equation in homogeneous Besov spaces View the MathML sourceḂp,rs(Rn) with s<0s<0. The nonlinear estimate is established by means of the Littlewood–Paley trichotomy and is used to prove the global well-posedness of solutions for small initial data in the homogeneous Besov space View the MathML sourceḂp,rs(Rn) with s=n/p−2/b<0s=n/p−2/b<0. In particular, when r=∞r=∞ and the initial data φφ satisfies that View the MathML sourceλ2bφ(λx)=φ(x) for any λ>0λ>0, our result leads to the existence of global self-similar solutions to the problem.