# A Priori Tame Estimates in Sobolev Spaces for the Plasma–Vacuum Interface Problem

## Abstract

We study the free boundary problem for the plasma–vacuum interface in the case where the plasma density is strictly positive up to the boundary. For the linearized problem we derive the so-called tame estimates which can be used for proving the existence of solutions to the nonlinear problem by the Nash-Moser method.

- Authors:

- Sobolev Institute of Mathematics SB RAS (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22771399

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 230; Journal Issue: 1; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; INTERFACES; MATHEMATICAL SOLUTIONS; MATHEMATICAL SPACE; NONLINEAR PROBLEMS; PLASMA DENSITY; PRESSURE RANGE MICRO PA

### Citation Formats

```
Mandrik, N. V., E-mail: manikitos@gmail.com.
```*A Priori Tame Estimates in Sobolev Spaces for the Plasma–Vacuum Interface Problem*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3732-1.

```
Mandrik, N. V., E-mail: manikitos@gmail.com.
```*A Priori Tame Estimates in Sobolev Spaces for the Plasma–Vacuum Interface Problem*. United States. doi:10.1007/S10958-018-3732-1.

```
Mandrik, N. V., E-mail: manikitos@gmail.com. Sun .
"A Priori Tame Estimates in Sobolev Spaces for the Plasma–Vacuum Interface Problem". United States. doi:10.1007/S10958-018-3732-1.
```

```
@article{osti_22771399,
```

title = {A Priori Tame Estimates in Sobolev Spaces for the Plasma–Vacuum Interface Problem},

author = {Mandrik, N. V., E-mail: manikitos@gmail.com},

abstractNote = {We study the free boundary problem for the plasma–vacuum interface in the case where the plasma density is strictly positive up to the boundary. For the linearized problem we derive the so-called tame estimates which can be used for proving the existence of solutions to the nonlinear problem by the Nash-Moser method.},

doi = {10.1007/S10958-018-3732-1},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 1,

volume = 230,

place = {United States},

year = {2018},

month = {4}

}

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