ScholarLens Back to search
2022•AIP conference proceedingsRequires access

On the well-posedness in Lorentz spaces for the inhomogeneous heat equation

Elena Nikolova, Mirko Tarulli, George Venkov

Open publisher page 0 citations

Abstract

We present new Strichartz estimates in Lorentz spaces for the solutions to the heat equation with inhomogeneous nonlinearity in the mass subcritical framework and space dimension d ≥ 1. As an application we prove local and global well-posedness in the Strichartz-Lorentz space Lq((0, T ); Lr,2(ℝd)), both in the focusing and the defocusing case, assuming the initial data are in the L2(ℝd) space.

About this research paper

What this paper is about

We present new Strichartz estimates in Lorentz spaces for the solutions to the heat equation with inhomogeneous nonlinearity in the mass subcritical framework and space dimension d ≥ 1. As an application we prove local and global well-posedness in the Strichartz-Lorentz space Lq((0, T ); Lr,2(ℝd)), both in the focusing and the defocusing case, assuming the initial data are in the L2(ℝd) space.

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

We present new Strichartz estimates in Lorentz spaces for the solutions to the heat equation with inhomogeneous nonlinearity in the mass subcritical framework and space dimension d ≥ 1. As an application we prove local and global well-posedness in the Strichartz-Lorentz space Lq((0, T ); Lr,2(ℝd)), both in the focusing and the defocusing case, assuming the initial data are in the L2(ℝd) space.

Key concepts: Lorentz transformation, Dimension (graph theory), Lorentz space, Space (punctuation), Hyperboloid model, Heat equation, Physics, Mathematical analysis

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
On the well-posedness in Lorentz spaces for the inhomogeneous heat equation — Research Paper | ScholarLens