José L. Rodrigo

activity

20132026

most citedLocal existence for the non-resistive MHD equations in nearly optimal Sobolev spaces

128 citations · 192 across the 14 of their papers we have counts for

collaborators

19 papers

math.AP2026

Bounds on the growth of high Sobolev norms of solutions to the fractional nonlinear Schrödinger equation on $R^{2}$ and $R^{3}$

Antonios Kapetanios, José L. Rodrigo, Vedran Sohinger

We prove polynomial bounds on the growth of high Sobolev norms of solutions to the defocusing fractional nonlinear Schrödinger equation with cubic and Hartree-type nonlinearities i…

math.AP2023

The adjoint Rayleigh and Orr-Sommerfeld equations: Green function and eigenmodes

Lorenzo Quarisa, José L. Rodrigo

The Rayleigh and Orr-Sommerfeld equations are ODEs which arise from the linearized Euler and Navier-Stokes equation around a shear flow. In this paper, we consider the adjoints of…

math.AP2021★ 5 cited

Instability of Boundary Layers with the Navier Boundary Condition

Lorenzo Quarisa, José L. Rodrigo

We study the $L^{\infty}$ stability of the 2D Navier-Stokes equations with a viscosity-dependent Navier boundary condition around shear profiles which are linearly unstable for the…

math.AP2021

On 2D Harmonic Extensions of Vector Fields and Stellarator Coils

Adam J. Golab, James C. Robinson, José L. Rodrigo

We consider a problem relating to magnetic confinement devices known as stellarators. Plasma is confined by magnetic fields generated by current-carrying coils, and here we investi…

math.AP2020

Remarks on a nonlocal transport

Dong Li, Jose Rodrigo

We consider a one dimensional nonlocal transport equation and its natural multi-dimensional analogues. By using a new pointwise inequality for the Hilbert transform, we give a shor…

math.AP2020

Local Existence of Analytic Sharp Fronts for Singular SQG

Calvin Khor, José L. Rodrigo

In this paper, we prove local existence and uniqueness of analytic sharp-front solutions to a generalised SQG equation by the use of an abstract Cauchy--Kowalevskaya theorem. Here,…

math.AP2020

On Sharp Fronts and Almost-Sharp Fronts for singular SQG

Calvin Khor, José L. Rodrigo

In this paper we consider a family of active scalars with a velocity field given by $u = Λ^{- 1 + α} \nabla^{⊥} θ$ , for $α \in (0, 1)$ . This family of equations is a more singular ve…

math.AP2019★ 3 cited

Non-conservation of dimension in divergence-free solutions of passive and active scalar systems

Charles L. Fefferman, Benjamin C. Pooley, José L. Rodrigo

For any $h \in (1, 2]$ , we give an explicit construction of a compactly supported, uniformly continuous, and (weakly) divergence-free velocity field in $R^{2}$ that weakly adve…

math.AP2019

Asymptotics for vortex filaments using a modified Biot-Savart kernel

Benjamin C. Pooley, José L. Rodrigo

We consider a family of approximations to the Euler equations obtained by adding $(- Δ)^{- α /2}$ to the non-locality in the Biot-Savart kernel together with a mollification (with par…

math.AP2019★ 14 cited

On the singularity formation and relaxation to equilibrium in 1D Fokker-Planck model with superlinear drift

José A. Carrillo, Katharina Hopf, José L. Rodrigo

We consider a class of Fokker--Planck equations with linear diffusion and superlinear drift enjoying a formal Wasserstein-like gradient flow structure with convex mobility function…

math.AP2018

Energy conservation for the Euler equations on $T^{2} \times R_{+}$ for weak solutions defined without reference to the pressure

James C. Robinson, José L. Rodrigo, Jack W. D. Skipper

We study weak solutions of the incompressible Euler equations on $T^{2} \times R_{+}$ ; we use test functions that are divergence free and have zero normal component, t…

math.AP2017★ 16 cited

Aggregation equations with fractional diffusion: preventing concentration by mixing

Katharina Hopf, José L. Rodrigo

We investigate a class of aggregation-diffusion equations with strongly singular kernels and weak (fractional) dissipation in the presence of an incompressible flow. Without the fl…

math.AP2016★ 4 cited

Energy conservation in the 3D Euler equations on $T^{2} \times R_{+}$

James C. Robinson, José L. Rodrigo, Jack W. D. Skipper

The aim of this paper is to prove energy conservation for the incompressible Euler equations in a domain with boundary. We work in the domain $T^{2} \times R_{+}$ , wher…

math.AP2016★ 128 cited

Local existence for the non-resistive MHD equations in nearly optimal Sobolev spaces

Charles L. Fefferman, David S. McCormick, James C. Robinson +1

This paper establishes the local-in-time existence and uniqueness of solutions to the viscous, non-resistive magnetohydrodynamics (MHD) equations in $R^{d}$ , $d = 2, 3$ , with i…

math.AP2015★ 1 cited

Lower bounds on blowing-up solutions of the 3D Navier--Stokes equations in $H ˙^{3/2}$ , $H ˙^{5/2}$ , and $B ˙_{2, 1}^{5/2}$

David S. McCormick, Eric J. Olson, James C. Robinson +3

If $u$ is a smooth solution of the Navier--Stokes equations on $R^{3}$ with first blowup time $T$ , we prove lower bounds for $u$ in the Sobolev spaces $H ˙^{3/2}$ , $\dot…

math.AP2015

Local existence for the non-resistive MHD equations in Besov spaces

Jean-Yves Chemin, David S. McCormick, James C. Robinson +1

In this paper we prove the existence of solutions to the viscous, non-resistive magnetohydrodynamics (MHD) equations on the whole of $R^{n}$ , $n = 2, 3$ , for divergence-free…

math.AP2014★ 1 cited

Higher order commutator estimates and local existence for the non-resistive MHD equations and related models

C. L. Fefferman, D. S. McCormick, J. C. Robinson +1

This paper establishes the local-in-time existence and uniqueness of strong solutions in $H^{s}$ for $s > n /2$ to the viscous, non-resistive magnetohydrodynamics (MHD) equations in…

math.AP2013★ 20 cited

Existence and uniqueness for a coupled parabolic-elliptic model with applications to magnetic relaxation

David S. McCormick, James C. Robinson, Jose L. Rodrigo

We prove existence, uniqueness and regularity of weak solutions of a coupled parabolic-elliptic model in two dimensions; we consider the standard equations of magnetohydrodynamics…

math.AP2013

Generalised Gagliardo-Nirenberg inequalities using weak Lebesgue spaces and BMO

David S. McCormick, James C. Robinson, Jose L. Rodrigo

Using elementary arguments based on the Fourier transform we prove that for $1 \leq q < p < \infty$ and $s \geq 0$ with $s > n (1/2 - 1/ p)$ , if $f \in L^{q,\infty}(\R^n) \cap \dot{H}^…

Bounds on the growth of high Sobolev norms of solutions to the fractional nonlinear Schrödinger equation on R2 and R3

The adjoint Rayleigh and Orr-Sommerfeld equations: Green function and eigenmodes

Instability of Boundary Layers with the Navier Boundary Condition

On 2D Harmonic Extensions of Vector Fields and Stellarator Coils

Remarks on a nonlocal transport

Local Existence of Analytic Sharp Fronts for Singular SQG

On Sharp Fronts and Almost-Sharp Fronts for singular SQG

Non-conservation of dimension in divergence-free solutions of passive and active scalar systems

Asymptotics for vortex filaments using a modified Biot-Savart kernel

On the singularity formation and relaxation to equilibrium in 1D Fokker-Planck model with superlinear drift

Energy conservation for the Euler equations on T2×R+​ for weak solutions defined without reference to the pressure

Aggregation equations with fractional diffusion: preventing concentration by mixing

Energy conservation in the 3D Euler equations on T2×R+​

Local existence for the non-resistive MHD equations in nearly optimal Sobolev spaces

Lower bounds on blowing-up solutions of the 3D Navier--Stokes equations in H˙3/2, H˙5/2, and B˙2,15/2​

Local existence for the non-resistive MHD equations in Besov spaces

Higher order commutator estimates and local existence for the non-resistive MHD equations and related models

Existence and uniqueness for a coupled parabolic-elliptic model with applications to magnetic relaxation

Generalised Gagliardo-Nirenberg inequalities using weak Lebesgue spaces and BMO

Bounds on the growth of high Sobolev norms of solutions to the fractional nonlinear Schrödinger equation on $R^{2}$ and $R^{3}$

Energy conservation for the Euler equations on $T^{2} \times R_{+}$ for weak solutions defined without reference to the pressure

Energy conservation in the 3D Euler equations on $T^{2} \times R_{+}$

Lower bounds on blowing-up solutions of the 3D Navier--Stokes equations in $H ˙^{3/2}$ , $H ˙^{5/2}$ , and $B ˙_{2, 1}^{5/2}$