Multi-dimensional Burgers equation with unbounded initial data: well-posedness and dispersive estimates

By introducing a Bourgain space associated to the usual KPI equation (re- lated only to the dispersive part of the linear symbol in the KPBI equation), Molinet-Ribaud [14] had

Weissler, Asymptotically self-similar global solutions of a general semilinear heat equation, Math. Xu, Existence and nonexistence of global solutions for a semilinear heat

2 Key words; anyon, Haldane statistics, low temperature kinetic theory, quantum Boltzmann equation.... Here dω corresponds to the Lebesgue probability measure on

Remark 2.3. In view of Theorem 2.4, there exists a global classical solution u ε from each of those mollified initial conditions. The only remaining problem is to restore the

As we have seen in [5], [6], and [7], when the Rossby number ε goes to zero, the system is stabilized as its solutions go to the solutions of the quasigeostrophic model (We refer

The key point is that we cut the initial data into two parts : the first part being regular enough to apply theorem 3, and the second one being H ˙ 1 2 with small initial data, in

[1] Gregory R. Baker, Xiao Li, and Anne C. Analytic structure of two 1D-transport equations with nonlocal fluxes. Bass, Zhen-Qing Chen, and Moritz Kassmann. Non-local Dirichlet

Concerning the data completion problem, we have obtained several results such as the existence of a solution and we have introduced a Tikhonov regularization in order to deal with