Publications

1. The three dimensional magneto-hydrostatic equations with Grad-Rubin boundary value. (with D. Sánchez-Simón del Pino and J. J. L. Velázquez),  Submitted, 2024..

2. Well-posedness and decay for a nonlinear propagation wave model in atmospheric flows. (with R. Granero-Belinchón),  Submitted, 2024.                                                                       

3. Well-posedness for an hyperbolic-hyperbolic-elliptic system describing cold plasmas. (with R. Granero-Belinchón)

Applied Mathematical Letters, 147, 108863, (2024) - arXiv 

4. Derivation and well-posedness of asymptotic models for cold plasmas. (with Á. Durán and R. Granero-Belinchón)

Nonlinear Analysis, 244, 113539, (2024) - arXiv  

5. Rotating solutions to the incompressible Euler-Poisson equation with external particle. (with B. Kepka and J. J. L. Velázquez), 

 Accepted in Annales de l'Institut Henri Poincaré C: Analyse non linéaire, (2024).

6. Global existence and blow-up for a stochastic transport equation with non-local velocity.  (with Y. Miao and H. Tang)

Journal of Differential Equations, 335, 244-293, (2022)-arXiv 

7. On the Grad-Rubin boundary value problem for the two-dimensional magneto-hydrostatic equations. (with J. J. L. Velázquez) 

 Mathematische Annalen, 388, 2387-247, (2024) -arXiv   

8. Global existence and decay of the inhomogeneous Muskat problem with Lipschitz initial data. (with R. Granero-Belinchón)

Nonlinearity, 35, 9 4749-4778, (2022)-arXiv 

9. On the blow up of a non-local transport equation in compact manifolds. (with A. D. Martínez )

Proc. Amer. Math. Soc. 151, 723-735, (2023) -arXiv 

10. Boundary value problems for steady incompressible fluids.  (with J. J.L. Velázquez) 

Journal of Differential Equations, 307, 211-249 (2022) - arXiv 

11. A local-in-time theory for singular SDEs with applications to fluid models with transport noise.  (with H. Tang and C. Rohde) 

Journal of Nonlinear Science, 31, 98 (2021) - arXiv 

12. Asymptotic shallow models arising in magnetohydrodynamics.  

Water Waves, 3 371–398 (2021) - arXiv 

13. Modelling the climate and weather of a 2D Lagrangian-averaged Euler-Boussinesq equation with transport noise (with A. Bethencourt de León, D. Holm, and S. Takao) Journal of Statistical Physics, 179 1267–1303 (2020) - arXiv 

14. The Burgers' equation with stochastic transport: shock formation, local and global existence of smooth solutions (with A. Bethencourt de León and S. Takao)  Nonlinear Differential Equations and Applications 26 no. 6, 1-33 (2019)- arXiv 

15. Pointwise monotonicity of heat kernels.  (with F. Chamizo, A.D. Martínez and A. Mas) 

Revista Matemática Complutense, 1-14, (2021)- arXiv 

16.  On the well-posedness of stochastic Boussinesq equations with cylindrical multiplicative noise (with. A. Bethencourt de León)                                                               Journal of Nonlinear Science 30 no. 1, 175–224 (2020) -  arXiv 

17. Stability, well-posedness and blow-up criterion for the Incompressible Slice Model (with A. Bethencourt de León)

 Physica D: Nonlinear Phenomena 392, 99-118 (2019) - arXiv 

18. Global well-posedness of critical surface quasigeostrophic equation on the sphere  (wih A. Córdoba and A.D. Martínez)  

Advances in Mathematics, 328 248–263 (2018) - arXiv 

19. Continuity of weak solutions of the critical surface quasigeostrophic equation on the sphere (wih A. Córdoba and A.D. Martínez)  Advances in Mathematics, 328 264–299 (2018) - arXiv 

20. Integral representation for fractional Laplace-Beltrami operators (wih A. Córdoba and A.D. Martínez)

 Advances in Mathematics, 328 436–445 (2018) -  arXiv 

Proceedings

1. Free boundary problems arising in fluid mechanics (with C. García and J. J.L.  Velázquez)

Oberwolfach Reports, 11/2023 (2023).