2025/05/17 by Thomas Duyckaerts, Duyckaerts, Thomas, Tristan Roy +1
Mathematics · #35B40 #35L15 #35L52 #35L71 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2505.11931
openalex publication_date 2025/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work concerns a general system of energy-critical wave equations in the Minkowski space of dimension 1+3. The wave equations are coupled by the nonlinearities, which are homogeneous of degree 5. We prove that any radial solution of the system can be written asymptotically as a sum of rescaled stationary solutions plus a radiation term, along any sequence of times for which the solution is bounded in the energy space. With an additional structural assumption on the nonlinearity, we prove a continuous in time resolution result for radial solutions. The proof of the sequential resolution uses the channel of energy method, as in the scalar case treated by Duyckaerts, Kenig and Merle (Cambridge Journal of Mathematics 2013 and arXiv 1204.0031). The proof of the continous in time resolution is based on new compactness and localization arguments.