Published

A priori bounds for rough differential equations with a non-linear damping term, joint work with Ajay Chandra, Augustin Moinat, and Hendrik Weber. Journal of Differential Equations, Vol. 318 p58-93, May 2022

Abstract: We consider a rough differential equation with a non-linear damping drift term: dY(t) = -|Y|^{m-1} Y(t) dt + σ(Y(t)) dX(t), where X is a branched rough path of arbitrary regularity α>0, m>1 and where σ is smooth and satisfies an m and α-dependent growth property. We show a strong a priori bound for Y, which includes the "coming down from infinity" property, i.e. the bound on Y(t) for a fixed t>0 holds uniformly over all choices of initial datum Y(0). The method of proof builds on recent work by Chandra, Moinat and Weber on a priori bounds for the φ^4 SPDE in arbitrary subcritical dimension. A key new ingredient is an extension of the algebraic framework which permits to derive an estimate on higher order conditions of a coherent controlled rough path in terms of the regularity condition at lowest level.

Bibtex

  @Article{BCMW2022,
          author = {Bonnefoi, Timothée and Chandra, Ajay and Moinat, Augustin and Weber, Hendrik},
          title = {A priori bounds for rough differential equations with a non-linear damping term},
          issn = {0022-0396},
          pages = {58--93},
          volume = {318},
          date = {2022-05},
          doi = {10.1016/j.jde.2022.02.006},
          journaltitle = {Journal of Differential Equations},
  }